We show that there is a computable procedure which, given an ∀∃-sentence ${\varphi}$ in the language of the partially ordered sets with a top element 1 and a bottom element 0, computes whether ${\varphi}$ is true in the Medvedev degrees of ${\Pi^0_1}$ classes in Cantor space, sometimes denoted by ${\mathcal{P}_s}$.

In this article, we study an analogue of tt-reducibility for points in computable metric spaces. We characterize the notion of the metric tt-degree in the context of first-level Borel isomorphism. Then, we study this concept from the perspectives of effective topological dimension theory and of effective fractal dimension theory.

Neoliberal reforms have changed the conduct of academic research in, and beyond, science, technology and society. Social science scholars have undertaken critical studies regarding the negative consequences of neoliberalism, such as the globalization of poverty and the inattention to rights and fairness. However, science and technology studies (STS), which should take a critical approach to science and technology, has generally not addressed the problem of neoliberalism. Rather, some currents in STS may be viewed as supportive of neoliberal transformations. 1 Why (...) is this so? To address this question, Japanese public policy will provide a case study. In Japan, public policy changed, affected by neoliberal reforms in the 1990s. Consequently, a broad area of Japanese social sciences was altered regarding how to be engaged in public policy. STS in Japan was formed at this time and shifted to neoliberal public policy. As a result STS, as well as many other social sciences, transformed their critical function. These circumstances seem to have overlapped and caused STS in Japan to be uncritical of neoliberalism. (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)

Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class $$\Gamma$$, then its $$\Gamma$$ -code can be obtained from its Borel code in a hyperarithmetical manner. We extend Louveau’s theorem to Borel functions: If a Borel function on a Polish space happens to be a $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -function, then one can find its $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -code hyperarithmetically relative to its Borel code. More generally, we prove (...) extension-type, domination-type, and decomposition-type variants of Louveau’s theorem for Borel functions. (shrink)

A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $\mathbf {0}'$ -computable low $_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high $_{n}$ -degrees are required to present the homeomorphism type of $X_n$. (...) Along the way we investigate the computable aspects of Čech homology groups. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. (shrink)

We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a separable metrizable space. Our techniques employ deep results from effective descriptive set theory and recursion theory. In fact it is essential to extend several prominent results in recursion theory (e.g. the Shore-Slaman Join Theorem) to the setting of Polish spaces. As a by-product we give both positive and negative results on (...) the Martin Conjecture on the degree preserving Borel functions between Polish spaces. Additionally we prove results about the transfinite version as well as the computable version of the Decomposability Conjecture. (shrink)

This article presents a unified theory of irony which claims, with the help of Fauconnier’s (1985) mental space theory, that an ironical utterance refers to the mental space of a mutually manifest expectation. According to this view, what a typical ironical speaker does is to say without any distinct space builders that something is the case in the mental space of expectation in order to make it mutually manifest that it is not so in the initial reality space. This expectation (...) space theory of irony integrates the explanatory power of Sperber and Wilson’s (1986) echoic interpretation theory with the descriptive power of the view of irony as relevant inappropriateness. (shrink)

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.

Consider a randomness notion C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. A uniform test in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is a total computable procedure that each oracle X produces a test relative to X in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. We say that a binary sequence Y is C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-random uniformly relative to (...) X if Y passes all uniform C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} tests relative to X. Suppose now we have a pair of randomness notions C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} and D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document} where C⊆D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C} \subseteq \mathcal{D}}$$\end{document}, for instance Martin-Löf randomness and Schnorr randomness. Several authors have characterized classes of the form Low which consist of the oracles X that are so feeble that C⊆DX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C} \subseteq \mathcal{D}^X}$$\end{document}. Our goal is to do the same when the randomness notion D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document} is relativized uniformly: denote by Low \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\star}$$\end{document} the class of oracles X such that every C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-random is uniformly D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document}-random relative to X. We show that X∈Low⋆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\in Low ^\star}$$\end{document} if and only if X is c.e. tt-traceable if and only if X is anticomplex if and only if X is Martin-Löf packing measure zero with respect to all computable dimension functions. We also show that X∈Low⋆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\in Low^\star}$$\end{document} if and only if X is computably i.o. tt-traceable if and only if X is not totally complex if and only if X is Schnorr Hausdorff measure zero with respect to all computable dimension functions. (shrink)

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing a detailed analysis of the Medvedev lattice of $\Sigma ^1_1$ -closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\Sigma ^1_1$ -choice principle on the integers. Harrington’s unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving this problem.

We prove the Decomposability Conjecture for functions of Baire class $2$ from a Polish space to a separable metrizable space. This partially answers an important open problem in descriptive set theory.

It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial Π10 subset of Cantor space. We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability. As for nonempty Π10 subsets of Cantor space, we show the existence of a finite-Δ20-piecewise degree containing infinitely many finite-2-piecewise degrees, and a finite-2-piecewise degree containing infinitely many finite-Δ20-piecewise degrees 2 denotes the difference of two Πn0 sets), whereas the greatest degrees in (...) these three “finite-Γ-piecewise” degree structures coincide. Moreover, as for nonempty Π10 subsets of Cantor space, we also show that every nonzero finite-2-piecewise degree includes infinitely many Medvedev degrees, every nonzero countable-Δ20-piecewise degree includes infinitely many finite-piecewise degrees, every nonzero finite-2-countable-Δ20-piecewise degree includes infinitely many countable-Δ20-piecewise degrees, and every nonzero Muchnik degree includes infinitely many finite-2-countable-Δ20-piecewise degrees. Indeed, we show that any nonzero Medvedev degree and nonzero countable-Δ20-piecewise degree of a nonempty Π10 subset of Cantor space have the strong anticupping properties. Finally, we obtain an elementary difference between the Medvedev degree structure and the finite-Γ-piecewise degree structure of all subsets of Baire space by showing that none of the finite-Γ-piecewise structures is Brouwerian, where Γ is any of the Wadge classes mentioned above. (shrink)

This paper examines the history of Japanese genetics in the 1920s to 1950s as seen through the work of Hitoshi Kihara, a prominent wheat geneticist as well as a leader in the development of the discipline in Japan. As Kihara's career illustrates, Japanese genetics developed quickly in the early twentieth century through interactions with biologists outside Japan. The interactions, however, ceased due to the war in the late 1930s, and Japanese geneticists were mostly isolated from outside information until (...) the late 1940s. During the isolation in wartime and under the postwar U.S. Occupation, Kihara adapted to political changes. During wartime, he developed a research institute focusing on applied biology of various crops, which conformed to the national need to address food scarcity. After the war, he led the campaign for the establishment of a national institute of genetics and negotiated with American Occupation officers. The Americans viewed this Japanese effort with suspicion because of the rising popularity of the controversial theory of the Russian agronomist, Trofim Lysenko, in Japan. The institute was approved in 1949 partly because Kihara was able to bridge the gap between the American and Japanese sides. With Kihara's flexible and generous leadership, Japanese genetics steadily developed, survived the wartime, and recovered quickly in the postwar period. The article discusses Kihara's interest in cytoplasmic inheritance and his synthetic approach to genetics in this political context, and draws attention to the relation between Kihara's genetics and agricultural practice in Japan. (shrink)

Neoliberalism advocates for the construction of free markets, which are to be used for solutions to economic and social problems rather than state solutions to those problems. Though Neoliberal reforms in Japan have affected its science and technology, STS literature has not focused on responses to neoliberalism through the lens of a country. Japan has a discrete STS history and Japan makes a good case study to the influence of neoliberalism on STS. In August 2010, at Tokyo’s Social Studies of (...) Science (4S) meetings, there were several sessions on neoliberalism and STS. At these sessions, Kunio Goto, Yasumoto Fujita, Hidetoshi Kihara, Hideto Nakajima, Steve Fuller, David Hess, Francis Remedios presented different responses to neoliberalism and STS. This special issue explores two themes. The first theme is Goto's and Fujita's call for a revitalization of Marxist STS as an alternative to the influence of neoliberalism on STS in Japan. The second theme is Kihara's and Nakajima's call for a revitalization of a critical function of STS in Japan. Hess examines STS as a field and its response to neoliberalism in Europe and Anglophone countries. (shrink)

The physician charter on medical professionalism creates standards of ethical behaviour for physicians and has been endorsed by professional organisations worldwide. It is based on the cardinal principles of the primacy of patient welfare, patient autonomy, and social welfare. There has been little discussion in the bioethics community of the doctrine of the charter and none from a Jewish ethical perspective. In this essay the authors discuss the obligations of the charter from a Jewish ethical viewpoint and call on other (...) cultures to develop their own unique perspectives on this important document. (shrink)

Moral education through service learning at post-secondary level is an important but under-researched field. Most existing studies center on its learning outcomes like academic progress, personal development, communication, and leadership skills, with only a few evaluating the moral development of college students participating in service-learning projects. The lack of study on moral development in service learning indicates a need for clarification of the theoretical underpinnings of service learning, John Dewey's ideas on moral growth, in particular his model of moral imagination (...) and the implications thereof, for current service-learning research and practice. We argue that Dewey's work here can help strengthen .. (shrink)

En la búsqueda de una ética para nuestro tiempo, el autor acude a la obra de Adorno para examinar la relación dialéctica entre praxis y teoría, y afirma que el nuevo concepto de praxis que emerge de esta relación podría guiarnos en la construcción de una ética más crítica que la mayoría de morales, constituidas únicamente por un sistema de normas. El autor defiende la concepción adorniana sobre el lugar del sujeto en la sociedad, que pretende despertar en este sujeto (...) la conciencia de sus capacidades, pero también de sus límites y sobre todo de su falta de libertad; lo que permite a Adorno conceder validez al intento de vida justa del sujeto moderno sólo en su problematicidad y fragilidad. (shrink)

In the real world, many people suffer as a function of their subordinate position in social hierarchy. Deliberative, relativist, and essentialist political theorists have sketched philosophies of social criticism that alone are inadequate for criticizing some harmful social values, practices, and norms. Certainly, theirs are critical theories in the sense that they are actionable, coherent, and self-reflective. But they are not adequate theories of social criticism. They do not specify satisfactorily the roles, qualifications, and methodology of social critics worried about (...) the struggles and wishes of real people. I specify all three. Drawing from the practical experience of a wide variety of women activists, I generalize about the roles and qualifications of the social critic. In addition, I formally articulate a method of social criticism that feminists have been developing. Collectively, feminists--particularly Third World women activists-have pioneered a method of social criticism that allows them to criticize existing social values, practices, and norms that perpetuate inequalities. The method of social criticism I propose provides a discipline for ongoing questioning and evaluation of social practices by a society with the help of social critics. In the process of explicating my own philosophy of social criticism, I offer criticisms of the implications for social criticism of three political philosophies--deliberative democratic theory, Michael Walzer's relativism, and Martha Nussbaum's essentialism--and argue that feminist critics have managed to achieve in practice what adherents of those three schools do incompletely in theory. (shrink)

We report a magnetization, magnetostriction, electrical resistivity, specific heat and neutron scattering study of a UNi 2/3 Rh 1/3 Al single crystal, a solid solution of an antiferromagnet UNiAl and a ferromagnet URhAl. The huge uniaxial magnetic anisotropy confining the principal magnetic response to the c axis in the parent compounds persists also for the solid solution. The magnetization curve at 1.6 K has a pronounced S shape with an inflection at 12 T. The temperature dependence of magnetic susceptibility exhibits (...) a maximum around 10 K and is magnetic history dependent at lower temperatures where the resistivity increases linearly with decreasing temperature. The low-temperature „ anomaly is removed in a magnetic field applied along c , which yields a large negative magnetoresistance amounting to m 46 z in 14 T . The C/T values exhibit a minimum around 12 K and below 8 K they become nearly constant , which is strongly affected by magnetic fields. Neutron scattering data confirm a non-magnetic ground state of UNi 2/3 Rh 1/3 Al. The bulk properties at low temperatures are tentatively attributed to the freezing of U magnetic moments with antiferromagnetic correlations. The additional intensities detected on top of nuclear reflections in neutron diffraction in a magnetic field applied along c are found to be proportional to the field-induced magnetization, which reflects field-induced ferromagnetic coupling of U magnetic moments. This scenario is corroborated also by finding low-temperature magnetostriction data that also scale with the square of magnetization. (shrink)