We define a notion of reducibility for subsets of a second countable T 0 topological space based on relatively continuous relations and admissible representations. This notion of reducibility induces a hierarchy that refines the Baire classes and the Hausdorff–Kuratowski classes of differences. It coincides with Wadge reducibility on zero dimensional spaces. However in virtually every second countable T 0 space, it yields a hierarchy on Borel sets, namely it is well founded and antichains are of length (...) at most 2. It thus differs from the Wadge reducibility in many important cases, for example on the real line $${\mathbb{R}}$$ or the Scott Domain $${\mathcal{P}\omega}$$. (shrink)

We prove that the Wadge order on the Borel subsets of the Scott domain is not a well-quasi-order, and that this feature even occurs among the sets of Borel rank at most 2. For this purpose, a specific class of countable 2-colored posets$\mathbb{P}_{emb} $equipped with the order induced by homomorphisms is embedded into the Wadge order on the$\Delta _2^0 $-degrees of the Scott domain. We then show that$\mathbb{P}_{emb} $admits both infinite strictly decreasing chains and infinite antichains with respect (...) to this notion of comparison, which therefore transfers to the Wadge order on the$\Delta _2^0 $-degrees of the Scott domain. (shrink)

We consider Borel sets of finite rank $A \subseteq\Lambda^\omega$ where cardinality of Λ is less than some uncountable regular cardinal K. We obtain a "normal form" of A, by finding a Borel set Ω, such that A and Ω continuously reduce to each other. In more technical terms: we define simple Borel operations which are homomorphic to ordinal sum, to multiplication by a countable ordinal, and to ordinal exponentiation of base K, under the map which sends every Borel set A (...) of finite rank to its Wadge degree. (shrink)

Let A and B be subsets of the space 2 N of sets of natural numbers. A is said to be Wadge reducible to B if there is a continuous map Φ from 2 N into 2 N such that A = Φ -1 (B); A is said to be monotone reducible to B if in addition the map Φ is monotone, that is, $a \subset b$ implies $\Phi (a) \subset \Phi(b)$ . The set A is said to be (...) monotone if a ∈ A and $a \subset b$ imply b ∈ A. For monotone sets, it is shown that, as for Wadge reducibility, sets low in the arithmetical hierarchy are nicely ordered. The ▵ 0 1 sets are all reducible to the (Σ 0 1 but not ▵ 0 1 ) sets, which are in turn all reducible to the strictly ▵ 0 2 sets, which are all in turn reducible to the strictly Σ 0 2 sets. In addition, the nontrivial Σ 0 n sets all have the same degree for n ≤ 2. For Wadge reducibility, these results extend throughout the Borel hierarchy. In contrast, we give two natural strictly Π 0 2 monotone sets which have different monotone degrees. We show that every Σ 0 2 monotone set is actually Σ 0 2 positive. We also consider reducibility for subsets of the space of compact subsets of 2 N . This leads to the result that the finitely iterated Cantor-Bendixson derivative D n is a Borel map of class exactly 2n, which answers a question of Kuratowski. (shrink)

If is a Polish metric space of dimension 0, then by Wadge’s lemma, no more than two Borel subsets of X are incomparable with respect to continuous reducibility. In contrast, our main result shows that for any metric space of positive dimension, there are uncountably many Borel subsets of that are pairwise incomparable with respect to continuous reducibility. In general, the reducibility that is given by the collection of continuous functions on a topological space \\) is (...) called the Wadge quasi-order for \\). As an application of the main result, we show that this quasi-order, restricted to the Borel subsets of a Polish space \\), is a well-quasiorder if and only if \\) has dimension 0. Moreover, we give further examples of applications of the construction of graph colorings that is used in the proofs. (shrink)

In this article, we propose a new classification of $\Sigma ^0_2$ formulas under the realizability interpretation of many-one reducibility (i.e., Levin reducibility). For example, $\mathsf {Fin}$, the decision of being eventually zero for sequences, is many-one/Levin complete among $\Sigma ^0_2$ formulas of the form $\exists n\forall m\geq n.\varphi (m,x)$, where $\varphi $ is decidable. The decision of boundedness for sequences $\mathsf {BddSeq}$ and for width of posets $\mathsf {FinWidth}$ are many-one/Levin complete among $\Sigma ^0_2$ formulas of the form (...) $\exists n\forall m\geq n\forall k.\varphi (m,k,x)$, where $\varphi $ is decidable. However, unlike the classical many-one reducibility, none of the above is $\Sigma ^0_2$ -complete. The decision of non-density of linear orders $\mathsf {NonDense}$ is truly $\Sigma ^0_2$ -complete. (shrink)

We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions).

In [9] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [9] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions).

We establish some results on the Borel and difference hierarchies in φ-spaces. Such spaces are the topological counterpart of the algebraic directed-complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non-collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω. We also sketch some older applications of these hierarchies and present a new application to the question of (...) characterizing the ω-ary Boolean operations generating a given level of the Wadge hierarchy from the open sets. (shrink)

Attempts to extend the classical Hausdorff difference hierarchy to the case of partitions of a space to k > 2 subsets lead to non‐equivalent notions. In a hope to identify the “right” extension we consider the extensions appeared in the literature so far: the limit‐, level‐, Boolean and Wadge hierarchies of k ‐partitions. The advantages and disadvantages of the four hierarchies are discussed. The main technical contribution of this paper is a complete characterization of the Wadge degrees of (...) Δ02‐measurable k ‐partitions of the Baire space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

The Axiom of Projective Determinacy implies the existence of a universal $\utilde{\Pi}^{1}_{n}\setminus\utilde{\Delta}^{1}_{n}$ set for every $n \geq 1$. Assuming $\text{\upshape MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\utilde{\Pi}^{1}_{1}\setminus\utilde{\Delta}^{1}_{1}$ set. In ZFC there is a universal $\utilde{\Pi}^{0}_{\alpha}\setminus\utilde{\Delta}^{0}_{\alpha}$ set for every $\alpha$.

In this thesis, we study the complexity of some mathematical problems: in particular, those arising in computable analysis and algorithmic learning theory for algebraic structures. Our study is not limited to these two areas: indeed, in both cases, the results we obtain are tightly connected to ideas and tools coming from different areas of mathematical logic, including for example descriptive set theory and reverse mathematics.After giving the necessary preliminaries, we first study the uniform computational strength of the Cantor–Bendixson theorem in (...) the Weihrauch lattice. This work falls into the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. We concentrate on problems related to perfect subsets of Polish spaces, studying the perfect set theorem, the Cantor–Bendixson theorem, and various problems arising from them. As far as we know, this is the first systematic study of problems at the level of $\mathbf {\Pi }^1_1\mathsf {-CA}_0$ in the Weihrauch lattice. We show that the strength of some of the problems we study depends on the topological properties of the Polish space under consideration, while others have the same strength once the space is rich enough.We continue considering problems related to (induced) subgraphs. We provide results on the (effective) Wadge complexity of sets of graphs, that are also used to determine the Weihrauch degree of certain decision problems. The decision problems we consider are defined for a fixed graph G, and they take as input a graph H, answering whether G is an (induced) subgraph of H: we also consider the opposite problem (i.e., answering whether H is an induced subgraph of G). We conclude this part on (induced) subgraphs considering the Weihrauch degree of “search problems.”These problems are defined for a fixed graph G, and they take as input a graph H such that G is an (induced) subgraph H: the output is a copy of G in H. In both cases, we highlight differences and analogies between the subgraph and the induced subgraph relation.We then move our attention to algorithmic learning theory, and we present the framework we use to study the learnability of families of algebraic structures: here, given a countable family of pairwise nonisomorphic structures $\mathfrak {K}$, a learner receives larger and larger pieces of an arbitrary copy of a structure in $\mathfrak {K}$ and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. We say that $\mathfrak {K}$ is learnable if there exists a learner which eventually stabilizes to a correct guess. The framework was lacking a method for comparing the complexity of nonlearnable families, and so we propose a solution to this problem using tools coming from invariant descriptive set theory. To do so, we first prove that a family of structures is learnable if and only if its learning domain is continuously reducible to the relation $E_0$ of eventual agreement on infinite binary sequences and then, replacing $E_0$ with Borel equivalence relations of higher complexity, we obtain a new hierarchy of learning problems. This leads to the notion of E-learnability, where a family of structures $\mathfrak {K}$ is E-learnable, for a Borel equivalence relation E, if there is a continuous reduction from the isomorphism relation associated with $\mathfrak {K}$ to E. It is then natural to ask how the notion of E-learnability interacts with “classical” learning paradigms.Finally, we study the number of mind changes that a learner needs to learn a given family, both from a topological and a combinatorial point of view, and we consider how the complexity of a learner (in terms of Turing reducibility) affects the number of mind changes for learning a given family.Abstract prepared by Vittorio Cipriani.E-mail: [email protected]: https://air.uniud.it/handle/11390/1252226. (shrink)

We study Polish spaces for which a set of possible distances $A \subseteq R^+$ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with distances in that set belong to a given (...) class, such as zero-dimensional, locally compact, etc. These results lead us to give a fairly complete description of the complexity, with respect to Borel reducibility and again depending on the properties of A, of the relations of isometry and isometric embeddability between these Polish spaces. (shrink)

Matthias Schröder has asked the question whether there is a weakest discontinuous problem in the topological version of the Weihrauch lattice. Such a problem can be considered as the weakest unsolvable problem. We introduce the discontinuity problem, and we show that it is reducible exactly to the effectively discontinuous problems, defined in a suitable way. However, in which sense this answers Schröder’s question sensitively depends on the axiomatic framework that is chosen, and it is a positive answer if we work (...) in Zermelo–Fraenkel set theory with dependent choice and the axiom of determinacy $\mathsf {AD}$. On the other hand, using the full axiom of choice, one can construct problems which are discontinuous, but not effectively so. Hence, the exact situation at the bottom of the Weihrauch lattice sensitively depends on the axiomatic setting that we choose. We prove our result using a variant of Wadge games for mathematical problems. While the existence of a winning strategy for Player II characterizes continuity of the problem (as already shown by Nobrega and Pauly), the existence of a winning strategy for Player I characterizes effective discontinuity of the problem. By Weihrauch determinacy we understand the condition that every problem is either continuous or effectively discontinuous. This notion of determinacy is a fairly strong notion, as it is not only implied by the axiom of determinacy $\mathsf {AD}$, but it also implies Wadge determinacy. We close with a brief discussion of generalized notions of productivity. (shrink)

We present an infinite-game characterization of the well-founded semantics for function-free logic programs with negation. Our game is a simple generalization of the standard game for negation-less logic programs introduced by van Emden [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3 37–53] in which two players, the Believer and the Doubter, compete by trying to prove a query. The standard game is equivalent to the minimum Herbrand model semantics of logic programming in the sense (...) that a query succeeds in the minimum model semantics iff the Believer has a winning strategy for the game which begins with the Doubter doubting this query. The game for programs with negation that we propose follows the same rules as the standard one, except that the players swap roles every time the play “passes through” negation. We start our investigation by establishing the determinacy of the new game by using some classical tools from the theory of infinite-games. Our determinacy result immediately provides a novel and purely game-theoretic characterization of the semantics of negation in logic programming. We proceed to establish the connections of the game semantics to the existing semantic approaches for logic programming with negation. For this purpose, we first define a refined version of the game that uses degrees of winning and losing for the two players. We then demonstrate that this refined game corresponds exactly to the infinite-valued minimum model semantics of negation [P. Rondogiannis,W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 441–467]. This immediately implies that the unrefined game is equivalent to the well-founded semantics. (shrink)

We present the design goals and metatheory of the Monadic Hybrid Calculus, a new formal system that has the same power as the Monadic Predicate Calculus. MHC allows quantification, including relative quantification, in a straightforward way without the use of bound variables, using a simple adaptation of modal logic notation. Thus “all Greeks are mortal” can be written as [G]M. MHC is also ‘hybrid’ in that it has individual constants, which allow us to formulate statements about particular individuals. Thus “Socrates (...) is Athenian and mortal” can be formalised as s.For our proof system, we use a simple adaptation of Beth-style tableaus. The availability of individual constants eliminates the need for labelled deduction.We discuss first the pragmatic and pedagogical advantages of MHC. Then we present the metatheory: formal syntax, semantics, proof rules, soundness, completeness and expressive equivalence with the Monadic Predicate Calculus. (shrink)

This article presents a new criticisms of reductive approaches to knowledge-‘wh’ (i.e., those approaches on which whether one stands in the knowledge-‘wh’ relation to a question is determined by whether one stands in the knowledge-‘that’ relation to some answer(s) to the question). It argues in particular that the truth of a knowledge-‘wh’ attribution like ‘Janna knows where she can buy an Italian newspaper’ depends not only on what Janna knows about the availability of Italian newspapers, but on what she believes (...) about the matter. This dependence of Janna's knowledge-‘wh’ on her (possibly false) beliefs is incompatible with the reductive approach. (shrink)

We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

In this paper we study the logical strength of the determinacy of infinite binary games in terms of second order arithmetic. We define new determinacy schemata inspired by the Wadge classes of Polish spaces and show the following equivalences over the system RCA0*, which consists of the axioms of discrete ordered semi‐rings with exponentiation, Δ10 comprehension and Π00 induction, and which is known as a weaker system than the popularbase theory RCA0: 1. Bisep(Δ10, Σ10)‐Det* ↔ WKL0, 2. Bisep(Δ10, Σ20)‐Det* (...) ↔ ATR0 + Σ11 induction, 3. Bisep(Σ10, Σ20)‐Det* ↔ Sep(Σ10, Σ20)‐Det* ↔ Π11‐CA0, 4. Bisep(Δ20, Σ20)‐Det* ↔ Π11‐TR0, where Det* stands for the determinacy of infinite games in the Cantor space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

Suppose that any two Π12 sets are comparable in the sense of Wadge degrees. Then every real has a dagger. This argument proceeds by using the Dodd-Jensen core model theory to show that x ε ωω along with, say, “0† implies the existence of a Π12 norm of length u2. As a result of more recent work by John Steel, the same argument will extend to show that the Wadge comparability of all Π12 sets implies Π12 determinacy.

This article is devoted to the conceptual analysis of two texts of leading scholars in cognitive neuroscience and its philosophy, Patricia Churchland and Eric Kandel. After a short introduction about the notion of reduction, I give a detailed account of the way both scientists view the relationship between theories about brain functioning on the one hand and consciousness and psychopathology, respectively, on the other hand. The analysis not only reveals underlying philosophical mind/brain conceptions and their inner tensions, but also the (...) conceptual relevance of distinctions that are fundamental in the work of Dooyeweerd, such as the distinction between modes and entities, between law and subject and between subject function and object function. After a brief clarification of the way these distinctions function in Dooyeweerd’s theory of the body as an ‘enkaptic structural whole’, I try to explain how the conceptual framework, developed here, could be applied to brain functioning and leads to greater clarity in neuroscientific theorizing. (shrink)

We show that, assuming the Axiom of Determinacy, every non-selfdual Wadge class can be constructed by starting with those of level $\omega _1$ and iteratively applying the operations of expansion and separated differences. The proof is essentially due to Louveau, and it yields at the same time a new proof of a theorem of Van Wesep. The exposition is self-contained, except for facts from classical descriptive set theory.

The present paper is part of a larger project of investigating how far puzzling questions about Carnap’s philosophical deflationism – as expressed most prominently in “Empricism, Semantics and Ontology”1 – can be answered by reference to his own preferred position in areas upon which this meta-philosophical position can be expected to have a bearing. For that project the explorations below provide a starting point; on the present occasion they will, I hope, be found to be of independent interest. At issue (...) is the question of what makes Carnap’s The Logical Structure of the World a pre-physicalist work. (shrink)

We show that the semi-linear ordering principle for continuous functions implies the determinacy of all Wadge and Lipschitz games.

We prove that the determinacy of all Lipschitz games, the determinacy of all Wadge games, and the semi-linear ordering principle for Lipschitz maps are all equivalent.

Reduced self-awareness is a well-known phenomenon investigated in patients with vascular disease; however, its impact on neuropsychological functions remains to be clarified. Importantly, selective vascular lesions provide an opportunity to investigate the key neuropsychological features of reduced self-awareness in neurocognitive disorders. Because of its rarity, we present an unusual case of a woman affected by a combined polar and paramedian bilateral thalamic infarction. The patient underwent an extensive neuropsychological evaluation to assess cognitive, behavioral, and functional domains, with a focus on (...) executive functions. She was assessed clinically in the acute phase and after 6 months from the stroke, both clinically and by magnetic resonance imaging. The patient developed a cognitive impairment, characterised by prevalent executive dysfunction associated with reduced self-awareness and mood changes, in terms of apathy and depression. Such condition persisted after 6 months. In May 2020, the patient underwent the serology test in chemiluminescence to detect IgG antibodies against SARS-CoV-2. The result of the quantitative test highlighted a high probability of previous contact with the virus. We suggest that reduced self-awareness related to executive dysfunction and behavioral changes may be due to combined polar and paramedian bilateral thalamic lesion. Metacognitive–executive dysfunction affecting the instrumental abilities of everyday life might make people less able to take appropriate precautions, facilitating the risk of SARS-CoV-2 contagion. (shrink)

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with (...) the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces. (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)

We investigate Borel reducibility between equivalence relations $E(X;p)=X^{\mathbb{N}}/\ell_{p}(X)'s$ where X is a separable Banach space. We show that this reducibility is related to the so called Hölder(α) embeddability between Banach spaces. By using the notions of type and cotype of Banach spaces, we present many results on reducibility and unreducibility between E(L r ; p)'s and E(c 0 ; p)'s for r, p ∈ [1, +∞). We also answer a problem presented by Kanovei in the affirmative by (...) showing that $\mathrm{C}\left({\mathrm{\mathbb{R}}}^{+}\right)/{\mathrm{C}}_{0}\left({\mathrm{\mathbb{R}}}^{+}\ri ght)$ is Borel bireducible to $\mathbb{R}^{\mathbb{N}}/c_{0}$. (shrink)

Mindfulness—the awareness of the present moment and experiences in daily life—contributes to genuine intrinsic and social-oriented values and curbs materialistic and hedonistic values. In the context of materialism, money is power. Avaricious individuals take risks and are likely to engage in dishonesty. Very little research has investigated the effects of mindfulness in reducing the avaricious monetary attitudes and enhancing ethical consumer beliefs. In this study, we theorize that mindfulness improves consumer ethics directly and indirectly by lowering avaricious monetary attitudes. To (...) test our theory, we collected data from 523 individuals with the Mindfulness-Based Stress Reduction training and 307 individuals without MBSR. The results of our whole sample support our theory. Three multiple-group confirmatory factor analyses reveal intriguing discoveries. First, with MBSR training, mindfulness excites consumer ethical beliefs directly and indirectly. Without training, trait mindfulness fails to reduce monetary attitudes—mindfulness training matters. Second, the power of MBSR training holds for participants completing the training within 1 year, but wears off after 1 year—the duration after training matters. Finally, after 1 year, the training retains its strength for those who practice mindfulness, but weakens its power for those who do not—practice matters. We shed light on mindfulness, monetary wisdom, and consumer ethics, in particular, and business ethics, in general. (shrink)

There is a clear need for interventions that reduce moral distress among healthcare providers (HCPs), given the high prevalence of moral distress and the far-ranging negative consequences it has for them. Healthcare ethics consultants are frequently called upon to manage moral distress, especially among nursing staff. Recently, researchers have both broadened the definition of moral distress and demarcated subcategories of the phenomenon with the intent of creating more targeted and effective interventions. One of the most frequently occurring subcategories of moral (...) distress in this new taxonomy has been labeled “moral-constraint distress,” though scholars have argued that not all constraints on HCPs’ moral agency are inappropriate given the often-competing healthcare values of patients, families, and clinical staff. To attempt to reduce the instances of moral distress in cases in which the constraints on HCPs’ moral agency are justified, we propose an intervention that focuses on shifting the HCPs’ “frame of reference” on moral-constraint distress, teaching HCPs how to distinguish unjustified and justified constraints on their moral agency. The anchors of this blueprint for reducing moral-constraint distress are the philosophical concepts of “values pluralism” and “values imposition.” The rationale for this intervention is that, in situations where the constraint on moral agency is justified but the experience of moral distress could nevertheless be severe, the emphasis needs to be on helping the HCP to “think differently” rather than “act differently.”. (shrink)

The effect of specificity of autobiographical memory (AM) retrieval on the affective impact of an emotional event was examined. In Study 1 (N = 90) the impact of a negative and positive experience was compared between student participants who habitually retrieve autobiographical memories (AMs) in a specific way and participants who generally retrieve less specific memories. In Study 2 (N = 48) the effect of an experimentally induced (specific vs. overgeneral) retrieval style on the impact of a negative experience was (...) studied in student participants who habitually retrieve less specific memories. Study 1 replicated the finding of Raes, Hermans, de Decker, Eelen, & Williams (Citation2003) that a negative event leads to less subjective distress in low‐specific participants as compared with high‐specific participants. However, both groups did not differ in their affective reaction to a positive event. Important, reduced memory specificity was associated with “repressive coping”, providing further evidence for the idea that reduced memory specificity is used as an avoidant or repressive‐defensive mechanism to regulate negative affect (CitationWilliams, 1996). In Study 2, participants who were induced to retrieve memories in an overgeneral way experienced more distress following a negative event as compared with participants who were induced to retrieve memories in a specific way. Results are discussed in the context of recent findings concerning AM specificity and emotion regulation (CitationPhilippot, Schaefer, & Herbette, 2003). Directions for further research are suggested. (shrink)

Music reduces pain in fibromyalgia (FM), a chronic pain disease, but the functional neural correlates of music-induced analgesia (MIA) are still largely unknown. We recruited FM patients ( n = 22) who listened to their preferred relaxing music and an auditory control (pink noise) for 5 min without external noise from fMRI image acquisition. Resting state fMRI was then acquired before and after the music and control conditions. A significant increase in the amplitude of low frequency fluctuations of the BOLD (...) signal was evident in the left angular gyrus (lAnG) after listening to music, which in turn, correlated to the analgesia reports. The post-hoc seed-based functional connectivity analysis of the lAnG showed found higher connectivity after listening to music with right dorsolateral prefrontal cortex (rdlPFC), the left caudate (lCau), and decreased connectivity with right anterior cingulate cortex (rACC), right supplementary motor area (rSMA), precuneus and right precentral gyrus (rPreG). Pain intensity (PI) analgesia was correlated ( r = 0.61) to the connectivity of the lAnG with the rPreG. Our results show that MIA in FM is related to top-down regulation of the pain modulatory network by the default mode network (DMN). (shrink)