Can visual interaction with artwork prompt healing? Can the brain recover from traumatic experiences and help heal the whole body? Since the 1940s, art therapists have claimed that the production of art can help heal past traumas. Similarly, occupational therapists have employed techniques from arts and crafts since the end of World War II to retrain soldiers helping them recover from the trauma of war. The global Covid-19 pandemic has caused health-related and psychological problems--isolation, increased anxiety, and fear--for people of (...) all ages, with the rates of such traumas affecting children tripling over the past two years. According to the Nebraska-based quilting company, Accuquilt, during the first six months of pandemic isolation in 2020, sales more than doubled as new customers showed a desire to participate in arts and crafts from home. This essay explores various approaches to the arts to determine how art may restore dignity and health following traumatic experiences. (shrink)

Scientific research is subject to a number of regulations which impose incidental (time, place), rather than substantive (type of research), restrictions on scientific research and the knowledge created through such research. In recent years, however, the premise that scientific research and knowledge should be free from substantive regulation has increasingly been called into question. Some have suggested that the law should be used as a tool to substantively restrict research which is dual-use in nature or which raises moral objections. There (...) are, however, some problems with using law to restrict or prohibit certain types of scientific research, including (i) the inherent imprecision of law for regulating complex and rapidly evolving scientific research; (ii) the difficulties of enforcing legal restrictions on an activity that is international in scope; (iii) the limited predictability of the consequences of restricting specific branches of scientific research; (iv) inertia in the legislative process; and (v) the susceptibility of legislators and regulators to inappropriate factors and influence. Rather than using law to restrict scientific research, it may be more appropriate and effective to use a combination of non-traditional legal tools including norms, codes of conduct, restrictions on publication, and scientist-developed voluntary standards to regulate problematic scientific research. (shrink)

Diverse beliefs about the nature and essence of scientific truth are pervasive in the nursing literature. Most recently, rejection of a more traditional and objective truth has resulted in a shift toward an emphasis on the acceptance of multiple and subjective truths. Some nursing scholars have discarded the idea that objective truth exists at all, but instead have argued that subjective truth is the only knowable truth and therefore the one that ought to govern nursing's disciplinary inquiry. Yet, there has (...) been relatively little critical debate or dialogue about the implications of adopting subjective and multiple truths as a maxim to govern the discipline. In this paper we examine what it might mean to adopt subjective forms of truth as the only knowable truths for nursing, and to accept the possibility of multiple co-existing realities. We understand the implications of such a philosophical stance for the epistemological basis of a practice science to be considerable, therefore we consider what it might mean for a practice-based discipline such as nursing to remain ambiguous on the question of truth, and examine the implications of failing to achieve consensus on what constitutes a truth claim. On the basis of this examination, we urge a cautious approach to the extremes of either position and argue for a more thoughtful and rigorous dialogue about ‘truth’ and knowledge in nursing practice, education, and research. (shrink)

The philosophy of patient-centred care has become widely embraced but its implementation is dependent on interrelated factors. A factor that has received limited attention is the role of policy tools. In Ontario, one method government can use to promote healthcare priorities is through health regulatory colleges, which set the standard of practice for health professionals. The degree to which government policy in support of patient-centered care has influenced the direction provided by health regulatory colleges to their members, and ultimately impacted (...) actual patient care, remains unclear. This study investigates the extent to which Ontario’s health regulatory colleges have provided explicit written guidance to members related to the importance of patient-centred care. It also explores applied and theoretical explanations that may further our understanding of why patient-centred care has not been more fully embraced. Findings reveal that guidance provided by Ontario’s health regulatory colleges varies widely. Institutional barriers and the choice of policy tools for disseminating government preferences may hinder full implementation of the principles of patient-centred care. More fully understanding the role health regulatory colleges’ play in facilitating the implementation of health policy will contribute positively to dialogue and to efforts to achieve positive health system reforms. (shrink)

Lack of guidance and regulation for authorizing medical cannabis for conditions involving the health and neurodevelopment of children is ethically problematic as it promulgates access inequities, risk-benefit inconsistencies, and inadequate consent mechanisms. In two virtual sessions using participatory action research and consensus-building methods, we obtained perspectives of stakeholders on ethics and medical cannabis for children and youth. The sessions focused on the scientific and regulatory landscape of medical cannabis, surrogate decision-making and assent, and the social and political culture of medical (...) cannabis. We found that evidence-gathering and data dissemination, pressures on clinical relationships, and the lack of integration of culturally diverse perspectives and Indigenous knowledges were key areas of concern. Participants emphasized the importance of utilizing adaptive study designs, highlighted the importance of trust-building between clinicians, patients and caregivers, and discussed barriers including historical and ongoing stigmatization of medical cannabis. We conclude that continued public consultation and strength-based research that integrate diverse perspectives are critical steps forward. (shrink)

In this paper, I shall suggest that, what Descartes supported in his letter to More of August 1649, when he claimed that God’s essence might be present everywhere, was not that God can’t exist without being extended, i.e. being omnipresent, but that God has necessarily the disposition to be extended. If my interpretation is correct, then the claim that God’s essence is omnipresent is consistent with the thesis that God is omnipresent ratione potentiæ.

We prove several trichotomy results for ideals of compact sets. Typically, we show that a "sufficiently rich" universally Baire ideal is either $\Pi _{3}^{0}$-hard, or $\Sigma _{3}^{0}$-hard, or else a σ-ideal.

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse similarity classes (...) under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

A function from Baire space to the natural numbers is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working in Bishop constructive mathematics: one is a function induced by a Brouwer‐operation (i.e., inductively defined neighbourhood function); the other is a function uniformly continuous near every compact image. We show that formal continuity is equivalent to the former while it is strictly (...) stronger than the latter. The equivalence of formally continuous functions and those induced by Brouwer‐operations requires Countable Choice. (shrink)

We show that every analytic set in the Baire space which is dominating contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. We call this property of analytic sets u-regularity. However, we show that the concept of uniform tree does not suffice to characterize dominating analytic sets in general. We construct a dominating closed set with the property that for no uniform tree whose (...) branches are contained in the closed set, the set of these branches is dominating. We also show that from a Σ1n+1-rapid filter a non-u-regular Π1n-set can be constructed. Finally, we prove that ∑12-Kσ-regularity implies ∑12-u-regularity. (shrink)

In Baire space N = ω ω we define a sequence of equivalence relations $\langle E_\nu| \nu , each E v being Σ 1 1 with classes in Π 0 1 + ν + 1 and such that (i) E ν does not have perfectly many classes, and (ii) N/E ν is countable iff $\omega^L_\nu . This construction can be extended cofinally in (δ 1 3 ) L . A new proof is given of a theorem of Hausdorff on partitions (...) of R into ω 1 many Π 0 3 sets. (shrink)

We propose a reformulation of the ideal $\mathcal {N}$ of Lebesgue measure zero sets of reals modulo an ideal J on $\omega $, which we denote by $\mathcal {N}_J$. In the same way, we reformulate the ideal $\mathcal {E}$ generated by $F_\sigma $ measure zero sets of reals modulo J, which we denote by $\mathcal {N}^*_J$. We show that these are $\sigma $ -ideals and that $\mathcal {N}_J=\mathcal {N}$ iff J has the Baire property, which in turn is equivalent to (...) $\mathcal {N}^*_J=\mathcal {E}$. Moreover, we prove that $\mathcal {N}_J$ does not contain co-meager sets and $\mathcal {N}^*_J$ contains non-meager sets when J does not have the Baire property. We also prove a deep connection between these ideals modulo J and the notion of nearly coherence of filters (or ideals). We also study the cardinal characteristics associated with $\mathcal {N}_J$ and $\mathcal {N}^*_J$. We show their position with respect to Cichoń’s diagram and prove consistency results in connection with other very classical cardinal characteristics of the continuum, leaving just very few open questions. To achieve this, we discovered a new characterization of $\mathrm {add}(\mathcal {N})$ and $\mathrm {cof}(\mathcal {N})$. We also show that, in Cohen model, we can obtain many different values to the cardinal characteristics associated with our new ideals. (shrink)

We investigate the tower spectrum in the generalized Baire space, i.e., the set of lengths of towers in $\kappa ^\kappa $. We show that both small and large tower spectra at all regular cardinals simultaneously are consistent. Furthermore, based on previous work by Bağ, the first author and Friedman, we prove that globally, a small tower spectrum is consistent with an arbitrarily large spectrum of maximal almost disjoint families. Finally, we show that any non-trivial upper bound on the tower spectrum (...) in $\kappa ^\kappa $ is consistent. (shrink)

This thesis is divided into three parts, the first and second ones focused on combinatorics and classification problems on discrete and geometrical objects in the context of descriptive set theory, and the third one on generalized descriptive set theory at singular cardinals of countable cofinality.Descriptive Set Theory (briefly: DST) is the study of definable subsets of Polish spaces, i.e., separable completely metrizable spaces. One of the major branches of DST is Borel reducibility, successfully used in the last 30 years to (...) solve and compare many classification problems. One of our goals is the classification of knots, very familiar and tangible objects in everyday life, which also play an important role in modern mathematics. The study of knots and their properties is known as knot theory. Our plan is to gain insight into knots using discrete objects, such as linear and circular orders. This approach was already exploited in [6]. The first part of this work is therefore devoted to countable linear orders and the study of the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results. We also expand our research to the case of circular orders.Another objective of this first part is to extend the notion of convex embeddability on countable linear orders. We provide a family of quasi-orders of which embeddability is a particular case as well. We study these quasi-orders from a combinatorial point of view and analyse their complexity with respect to Borel reducibility. Furthermore, we extend the analysis of these quasi-orders to the set of uncountable linear orders.The second part of the project deals with classification problems on knots and $3$ -manifolds. The goal here is to apply the results obtained in the first part to the study of proper arcs and knots, establishing lower bounds for the complexity of some natural relations between these geometrical objects. We also obtain some combinatorial results which are particularly interesting when we restrict to the set of wild proper arcs and wild knots, classes which haven’t received much attention so far. These parts are included in the two preprints [4, 5] in collaboration with my supervisor Alberto Marcone, Luca Motto Ros (University of Torino), and Vadim Weinstein (University of Oulu).The second part of this work also includes the classification of non-compact $3$ -manifolds up to homeomorphism (the case of compact $3$ -manifolds has already been solved: indeed, there are only countably many $3$ -manifolds up to homeomorphism; see [7]), and that of Cantor sets of $\mathbb {R}^3$ up to conjugation (answering to Question 5.5 of [3]). Here we resort to algebraic tools. Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras (see [1]). The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this work we introduce a weaker concept which we call “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration beyond totally disconnected. As an application of this method, we show that both homeomorphism on non-compact $3$ -manifolds and conjugation of Cantor sets in $\mathbb {R}^3$ are completely classifiable by countable structures. These results are part of an upcoming paper in collaboration with Vadim Weinstein.The last part of this thesis concerns the natural generalization of descriptive set theory that occurs when countable is replaced by uncountable, called Generalized Descriptive Set Theory (briefly: GDST). In particular, we focus on the case of GDST for a singular cardinal $\kappa $ of countable cofinality. The goal here is to study the generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $\mathcal {P}(\kappa )$. We consider the question under which large cardinal hypotheses classes of definable subsets of these spaces possess such regularity properties, focusing on rank-into-rank axioms, like I2, and classes of sets definable by $\Sigma _1$ -formulas with parameters from various collections of sets. The obtained results are included in [2], a joint work with my co-supervisor Vincenzo Dimonte and Philipp Lücke (University of Hamburg).Abstract prepared by Martina IannellaE-mail: [email protected]: https://air.uniud.it/handle/11390/1262824. (shrink)

The long-awaited revision of the industry standard on phylogenetics Since the publication of the first edition of this landmark volume more than twenty-five years ago, phylogenetic systematics has taken its place as the dominant paradigm of systematic biology. It has profoundly influenced the way scientists study evolution, and has seen many theoretical and technical advances as the field has continued to grow. It goes almost without saying that the next twenty-five years of phylogenetic research will prove as fascinating as the (...) first, with many exciting developments yet to come. This new edition of Phylogenetics captures the very essence of this rapidly evolving discipline. Written for the practicing systematist and phylogeneticist, it addresses both the philosophical and technical issues of the field, as well as surveys general practices in taxonomy. Major sections of the book deal with the nature of species and higher taxa, homology and characters, trees and tree graphs, and biogeography—the purpose being to develop biologically relevant species, character, tree, and biogeographic concepts that can be applied fruitfully to phylogenetics. The book then turns its focus to phylogenetic trees, including an in-depth guide to tree-building algorithms. Additional coverage includes: Parsimony and parsimony analysis Parametric phylogenetics including maximum likelihood and Bayesian approaches Phylogenetic classification Critiques of evolutionary taxonomy, phenetics, and transformed cladistics Specimen selection, field collecting, and curating Systematic publication and the rules of nomenclature Providing a thorough synthesis of the field, this important update to Phylogenetics is essential for students and researchers in the areas of evolutionary biology, molecular evolution, genetics and evolutionary genetics, paleontology, physical anthropology, and zoology. (shrink)

Computability theoretic aspects of Polish metric spaces are studied by adapting notions and methods of computable structure theory. In this dissertation, we mainly investigate index sets and classification problems for computably presentable Polish metric spaces. We find the complexity of a number of index sets, isomorphism problems, and embedding problems for computably presentable metric spaces. We also provide several computable structure theory results related to some classical Polish metric spaces such as the Urysohn space $\mathbb {U}$, the Cantor space $2^{\mathbb (...) {N}}$, the Baire space $\mathbb {N}^{\mathbb {N}}$, and spaces of continuous functions.Abstract prepared by Teerawat Thewmorakot.E-mail: [email protected]. (shrink)

Assume that the class of partial automorphisms of the monster model of a complete theory has the amalgamation property. The beautiful automorphisms are the automorphisms of models ofT which: 1. are strong, i.e. leave the algebraic closure (inT eq) of the empty set pointwise fixed, 2. are obtained by the Fraïsse construction using the amalgamation property that we have just mentioned. We show that all the beautiful automorphisms have the same theory (in the language ofT plus one unary function symbol (...) for the automorphism), and we study this theory. In particular, we examine the question of the saturation of the beautiful automorphisms. We also prove that in some cases (in particular if the theory is ω-stable andG-trivial), almost all (in the sense of Baire categoricity) automorphisms of the saturated countable model are beautiful and conjugate. (shrink)

We show that every dominating analytic set in the Baire space has a dominating closed subset. This improves a theorem of Spinas [15] saying that every dominating analytic set contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. In [15], a subset of the Baire space is called u-regular if either it is not dominating or it contains the branches of a uniform tree, (...) and it was proved that Σ21-Kσ-regularity implies Σ21-u-regularity. Here we show that these properties are in fact equivalent. Since the proof of analytic u-regularity uses a game argument it was clear that determinacy implies u-regularity of all sets. Here we show that an inaccessible cardinal is enough to construct a model for projective u-regularity, namely it holds in Solovay's model. Finally we show that forcing with uniform trees is equivalent to Laver forcing. (shrink)

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are ℝn, ℂn, Hilbert space and more generally all separable Banach spaces, the Cantor space 2ℕ, the Baire space ℕℕ, the infinite symmetric group S∞, the unitary group, the group of measure preserving transformations of the unit interval, etc.In this theory sets are (...) classified in hierarchies according to the complexity of their definitions and the structure of sets in each level of these hierarchies is systematically analyzed. In the beginning we have the Borel sets in Polish spaces, obtained by starting with the open sets and closing under the operations of complementation and countable unions, and the corresponding Borel hierarchy. After this come the projective sets, obtained by starting with the Borel sets and closing under the operations of complementation and projection, and the corresponding projective hierarchy.There are also transfinite extensions of the projective hierarchy and even much more complex definable sets studied in descriptive set theory, but I will restrict myself here to Borel and projective sets, in fact just those at the first level of the projective hierarchy, i.e., the Borel (), analytic () and coanalytic () sets. (shrink)

We show that any symmetric, Baire measurable function from the complement of $\ezero$ to a finite set is constant on an $\ezero$-nonsmooth square. A simultaneous generalization of Galvin's theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equivalence relations on $E_0$-nonsmooth sets, this result is proved by relating $\ezero$-nonsmooth sets to embeddings of the complete binary tree into itself and appealing to a version of Hindman's theorem on the complete binary tree. We also establish (...) several canonization theorems which follow from the main result. (shrink)

What is the nature of the intellectual enterprise - general equilibrium analysis - that so many economists regard as the centerpiece of their discipline? In this book, Roy Weintraub considers both the modern history of the analysis, and the methodological puzzles that it, and mathematical economic theory in general, pose. Professor Weintraub argues that previous writings on the history and method of general equilibrium theory have been curiously biased and misleading. He provides a clear and careful presentation of the development (...) of the theory from the 1930s through to the Arrow-Debreu work of the 1950s. This historical analysis is the centre of the book: a case study which permits the author to justify the status of general equilibrium theory in economics and the activity in which economic theorists engage. He argues that previous methodological investigations have been distorted by their use of inappropriate models taken from the philosophy of science that were developed to appraise work in the physical sciences. (shrink)

Interpretation of the classics in political theory seems to go in waves. For a while we had John Locke, the bourgeois thinker. Now we seem to be in a Locke-as-radical-democrat phase. Locke-the-bourgeois had problems of its own, but a radically democratic Locke -- not just the old Locke as liberal democrat but Locke as quasi-Leveller -- strains the interpretative imagination more than most; yet in recent years, several different kinds of argument have been advanced in support of it, both textual (...) and contextual. The most effective argument has proceeded by situating Locke in the context of radical Whig politics in the 1670s and '80s, the struggles over religious toleration and the royal succession, in particular the �Exclusion Crisis� of 1679-81. This contextual argument has been accompanied by various textual interpretations having to do with Locke's conceptions of property, consent, representation, the right of revolution and natural law. Among other things, these are supposed to show that while Locke had nothing explicit to say about the extent of the franchise, the weight of evidence suggests that he would have supported a fairly wide franchise, perhaps even something like the (almost) manhood suffrage advocated by the Levellers (at least according to some, and probably the most convincing, interpretations of their ideas). Most recently, in these pages, Martin Hughes, building on the work of James Tully and Richard Ashcraft in particular, has pushed the argument as far as it can probably go. His argument on taxation and suffrage has provided a motivation here for a wider exploration of Locke's views on representation, consent and the franchise. (shrink)

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite subsets of $\omega (...) $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

ObjectiveTo evaluate the relationship between recently trained paediatricians' ethics knowledge and exposure to a formal ethics or professionalism curriculum during residency.MethodsWe conducted a cross-sectional survey of recently trained paediatricians which included a validated 23-item instrument called the Test of Residents' Ethics Knowledge for Pediatrics. The sample included paediatricians who completed medical school in 2006–2008, whose primary specialty was paediatrics or a paediatric subspecialty, and who completed paediatric residency training in 2010–2011. This sample was stratified based on residency programme variables: presence (...) of a formal curriculum in ethics or professionalism, programme size and American Board of Pediatrics certifying exam passage rate. Paediatricians were randomly selected from each stratum for survey participation.ResultsAmong the 370 responding paediatricians (55%), the mean knowledge score was 17.3 (SD 2.2) out of a possible 23. Presence of a formal curriculum in ethics and/or professionalism was not significantly associated with knowledge. Knowledge was lowest on items about parental requests for a child to undergo genetic testing (2 items, 44% and 85% incorrect), preserving patient confidentiality over email (55% incorrect), decision-making regarding life-sustaining technologies (61% incorrect), and decision-making principles such as assent and parental permission (2 items, 47% and 49% incorrect).ConclusionsThis study highlights several areas in which paediatricians' knowledge may be low and that are amenable to targeted educational interventions. These findings should prompt discussion and research among ethicists and educators about how ethics and professionalism curricula can more consistently influence paediatricians' knowledge. (shrink)

This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open and (...) clopen Ramsey theorems. Since there is not a canonical way to phrase these theorems as multi-valued functions, we identify eight different multi-valued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility.We then discuss some new operators on multi-valued functions and study their algebraic properties and the relations with other previously studied operators on problems. In particular, we study the first-order part and the deterministic part of a problem f, capturing the Weihrauch degree of the strongest multi-valued problem that is reducible to f and that, respectively, has codomain $\mathbb {N}$ or is single-valued.These notions proved to be extremely useful when exploring the Weihrauch degree of the problem $\mathsf {DS}$ of computing descending sequences in ill-founded linear orders. They allow us to show that $\mathsf {DS}$, and the Weihrauch equivalent problem $\mathsf {BS}$ of finding bad sequences through non-well quasi-orders, while being very “hard” to solve, are rather weak in terms of uniform computational strength. We then generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level.Finally, we work in the context of geometric measure theory and we focus on the characterization, from the point of view of descriptive set theory, of some conditions involving the notions of Hausdorff/Fourier dimension and Salem sets. We first work in the hyperspace $\mathbf {K}$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbol {\Pi }^0_3$ -complete family. This is done by characterizing the complexity of the family of sets having sufficiently large Hausdorff or Fourier dimension. We also show that the complexity does not change if we increase the dimension of the ambient space and work in $\mathbf {K}$. We also generalize the results by relaxing the compactness of the ambient space and show that the closed Salem sets are still $\boldsymbol {\Pi }^0_3$ -complete when we endow $\mathbf {F}$ with the Fell topology. A similar result holds also for the Vietoris topology.We conclude by analyzing the same notions from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity, and show that the complexities remain the same also in the lightface case. In particular, we show that the family of all the closed Salem sets is $\Pi ^0_3$ -complete. We furthermore characterize the Weihrauch degree of the functions computing Hausdorff and Fourier dimension of closed sets.prepared by Manlio Valenti.E-mail:[email protected]. (shrink)

Today, economic theory is a mathematical theory, but that was not always the case. Major changes in the ways economists presented their arguments to one another occurred between the late 1930s and the early 1950s; over that period the discipline became mathematized. Professor Weintraub, a noted scholar of the modern history of economic thought, argues that those changes were not merely cosmetic: The mathematical forms of the arguments significantly altered the substance of the arguments. Stabilizing Dynamics is particularly concerned with (...) the ways in which the rich and confusing talk of the 1930s evolved, over a fifteen-year period, into technical analysis of some mathematical structures. The author describes the context for the history of that change, locating it in the broader intellectual currents, and shows how the history of modern economics can be seen as a confluence of several disparate traditions. Historiographically, this book offers one of the first constructivist accounts of modern economic analysis. (shrink)

Most authors who work with moral status automatically dismiss the possibility that plants are the kinds of entities that have moral status. This dismissal coheres with our intuitions about common-sense morality: if plants do not have moral status then we do not have any direct moral obligations to plant life. An implication of such a view is that any suggestion otherwise commits one to be in favour of an absurd conclusion. However, given the recent literature and empirical evidence on plant (...) minds, there are reasons to accept a different perspective that finds the absurd conclusion plausible. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

The wedge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). Here we extend the Wadge hierarchy of Borel sets to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces which implies e.g. several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces. In fact, (...) many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q. (shrink)

Let X, Y be Polish spaces,,. We say A is universal for Γ provided that each x‐section of A is in Γ and each element of Γ occurs as an x‐section of A. An equivalence relation generated by a set is denoted by, where. The following results are shown: If A is a set universal for all nonempty closed subsets of Y, then is a equivalence relation and. If A is a set universal for all countable subsets of Y, then (...) is a equivalence relation, and and ; if, then ; if every set is Lebesgue measurable or has the Baire property, then. for, if every set has the Baire property, and E is any equivalence relation, then. (shrink)

In this paper, we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals $s_0$, $m_0$, $l_0$, $cl_0$, $h_0,$ and $ch_0$. We show that there exists a subset of the Baire space $\omega ^\omega,$ which is s-, l-, and m-nonmeasurable that forms a dominating m.e.d. family. We investigate a notion of ${\mathbb {T}}$ -Bernstein sets—sets which intersect but do not contain any body of any tree from a given family of trees ${\mathbb {T}}$. We also obtain a (...) result on ${\mathcal {I}}$ -Luzin sets, namely, we prove that if ${\mathfrak {c}}$ is a regular cardinal, then the algebraic sum of a generalized Luzin set and a generalized Sierpiński set belongs to $s_0, m_0$, $l_0,$ and $cl_0$. (shrink)

We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three. In particular, this holds for the graph of the unilateral shift on [N]N, although its Borel chromatic number is N₀. We also show that if add(null) = c, then the universally measurable chromatic number of every treeing of a measure amenable equivalence relation is at most three. In (...) particular, this holds for "the" minimum analytic graph G₀ with uncountable Borel (and Baire measurable) chromatic number. In contrast, we show that for all κ ∈ {2, 3...., N₀. c}, there is a treeing of E₀ with Borel and Baire measurable chromatic number κ. Finally, we use a Glimm—Effros style dichotomy theorem to show that every basis for a non-empty initial segment of the class of graphs of Borel functions of Borel chromatic number at least three contains a copy of (R<N, ⊇). (shrink)

Why do so many of God’s followers seem to prefer their boxed-in religion over God? Listen to their rhetoric and you might wonder how a Supreme Being could be so narrow and small, so angry and unattractive. It’s time to start over with an honest conversation instead of a box. If God does exist, there should be some clear indications of his being. And if humans bear God’s image, as the Bible indicates, then we should be able to connect with (...) God on some level. This book is about God, not religion. It’s about questions more than watertight answers. It’s about the experience of God more than it is about incontrovertible evidence that he exists. God can’t be seen, but he can be found. And while he can’t be fully explained, he can be known and experienced. Religious boxes have a way of blinding us to spiritual reality. So this dialogue is all God, no box. Are you ready? (shrink)

Open peer commentary on the target article “From Objects to Processes: A Proposal to Rewrite Radical Constructivism” by Siegfried J. Schmidt. Upshot: The aim is to show that, although Schmidt’s thesis must in most respects be warmly welcomed, there is an unexpressed implication concerning the dialogic structure of language that, when drawn out plainly, reveals a further valuable move open to the theory. I offer it therefore as a clarification of his theory with which I hope Schmidt may agree. He (...) has already stressed the differences in understanding between one agent and another; it is because of this that, in order to communicate, agents must play without believing the mutual hypothetical projections of “truth,” “sincerity,” “objectivity,” “reference,” and other ideals of social “reality.” In the language process it is faith upon which this rests rather than blind trust. It is argued that only faith can properly take account of the risks of contingency. (shrink)

The fact that genes and environment contribute differentially to variation in human behaviors, traits and attitudes is central to the field of behavior genetics. Perceptions about these differential contributions may affect ideas about human agency. We surveyed two independent samples (N = 301 and N = 740) to assess beliefs about free will, determinism, political orientation, and the relative contribution of genes and environment to 21 human traits. We find that lay estimates of genetic influence on these traits cluster into (...) four distinct groups, which differentially predict beliefs about human agency, political orientation, and religiosity. Despite apparent ideological associations with these beliefs, the correspondence between mean lay estimates and published heritability estimates for the surveyed traits is large (r = .77). Belief in genetic determinism emerges as a modest predictor of accuracy in these lay estimates. Additionally, educated mothers with multiple children emerge as particularly accurate in their estimates of the genetic contribution to these traits. (shrink)

Reverse Mathematics (RM) is a program in the foundations of mathematics where the aim is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. Generally, the minimal axioms are equivalent to the theorem at hand, assuming a weak logical system called the base theory. Moreover, many theorems are either provable in the base theory or equivalent to one of four logical systems, together called the Big Five. For instance, the Weierstrass approximation theorem, i.e., that a (...) continuous function can be approximated uniformly by a sequence of polynomials, has been classified in RM as being equivalent to weak König’s lemma, the second Big Five system. In this paper, we study approximation theorems for discontinuous functions via Bernstein polynomials from the literature. We obtain many equivalences between the latter and weak König’s lemma. We also show that slight variations of these approximation theorems fall far outside of the Big Five but fit in the recently developed RM of new ‘big’ systems, namely the uncountability of ${\mathbb R}$, the enumeration principle for countable sets, the pigeon-hole principle for measure, and the Baire category theorem. (shrink)