異文化コミュニケーションのスキル、仕事の現場、技術者倫理など、グローバルエンジニアを志す人に必要な情報をまとめた一冊。.

There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

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)

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.

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 ${\mathcal{P}_s}$.

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)

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 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.

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)

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)

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)

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)

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.

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded learnability is equivalent to finite View the MathML source2-piecewise computability 2 denotes the difference of two View the MathML sourceΠ10 sets), error-bounded learnability is equivalent to finite View (...) the MathML sourceΔ20-piecewise computability, and learnability is equivalent to countable View the MathML sourceΠ10-piecewise computability . Second, we introduce disjunction-like operations such as the coproduct based on BHK-like interpretations, and then, we see that these operations induce Galois connections between the Medvedev degree structure and associated Medvedev/ Muchnik-like degree structures. Finally, we interpret these results in the context of the Weihrauch degrees and Wadge-like games. (shrink)

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)

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.

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)