Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still serves (...) to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable fan theorem is not (...) equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

The uniform continuity theorem states that every pointwise continuous real‐valued function on the unit interval is uniformly continuous. In constructive mathematics, is strictly stronger than the decidable fan theorem, but Loeb [17] has shown that the two principles become equivalent by encoding continuous real‐valued functions as type‐one functions. However, the precise relation between such type‐one functions and continuous real‐valued functions (usually described as type‐two objects) has been unknown. In this paper, we introduce an appropriate notion of continuity for a modulus (...) of a continuous real‐valued function on [0, 1], and show that real‐valued functions with continuous moduli are exactly those functions induced by Loeb's codes. Our characterisation relies on two assumptions: (1) real numbers are represented by regular sequences (equivalently Cauchy sequences with explicitly given moduli); (2) the continuity of a modulus is defined with respect to the product metric on the regular sequences inherited from the Baire space. Our result implies that is equivalent to the statement that every pointwise continuous real‐valued function on [0, 1] with a continuous modulus is uniformly continuous. We also show that is equivalent to a similar principle for real‐valued functions on the Cantor space. These results extend Berger's [2] characterisation of for integer‐valued functions on and unify some characterisations of in terms of functions having continuous moduli. (shrink)

徳川慶喜のブレーンにして明治政府の高級官僚。翻訳論、日本語論、軍事論。知の百面相・西周初の入門書。.

We correct a mistake in the paper “Generalized periodicity and primitivity for words” [4] and justify the existence of regular languages all of whose roots are not even context-sensitive.

Starting from six kinds of periodicity of words we define six sets of words which are primitive in different senses and we investigate their relationships. We show that only three of the sets are external Marcus contextual languages with choice but none of them is an external contextual language without choice or an internal contextual language. For the time complexity of deciding any of our sets by one-tape Turing machines, n2 is a lower bound and this is optimal in two (...) cases. The notions of roots and degrees of words and languages, which are strongly connected to periodicity and primitivity, are also considered, and we show that there can be an arbitrarily large gap between the complexity of a language and that of its roots. (shrink)

人の始期から終期の「生」について、生殖医療、再生医療、ゲノム医療などの先端医療を紹介し、バイオエシックス教育の実際をみる。.

With growing globalization, the governments of many countries are tending to place a disproportionately large emphasis on economy, which often results in budget cuts in health, education and social welfare. Such a tendency has provoked arguments by many individuals concerned. The neo-conservatism represented by ex-US President Reagan and ex-UK Prime Minister Thatcher in the 1980s, known as Reaganomics and Thatcherism, caused public funds for health care and education to be substantially reduced. In developing countries a so-called structural adjustment policy, promoted (...) by the World Bank and the International Monetary Fund, is leading to shrinking budgets for health, education and social security in general. (shrink)

A senior physician with a government role in Japan made a widely reported and misleading statement about Thailand’s policy on HIV/AIDS patients. He claimed that in Thailand the policy is to spend public money on the prevention of HIV infection while allowing AIDS patients to die untreated. The author, a community nursing specialist in Japan with first-hand knowledge of HIV/AIDS policy in Thailand, thought that this statement would influence attitudes negatively in Japan. However, speaking out about this misrepresentation of the (...) facts carried certain risks. Although freedom of expression is valued in Japan, in practice it is not easy to contradict senior medical professionals. The author uses his experience of this difficult professional situation to teach nurses how to approach speaking out in the public interest. (shrink)

Eukaryotic genes are divided into three categories according to the machineries by which they are transcribed. Ribosomal RNA genes (rDNA) are the only ones that are transcribed by RNA polymerase I and are under different control from other genes transcribed by RNA polymerase II or III. None the less, the regulation of rDNA is of prime interest in view of its close relationship to cell growth and differentiation. In this review I shall discuss the recent progress in the study of (...) transcription mechanisms of rDNA by the RNA polymerase I system. The structure of the rDNA promoter and the presence of possible upstream enhancer regions will be described. In addition, factors involved in the transcription initiation of this gene will be discussed with special reference to the formation of an initiation complex. (shrink)

Athletes in sport are not only physical beings but also spiritual beings. Sport is referred to sport as an issue of human self. What kind of inner self do athletes have in the context of modern sports? To consider the issue of self in sport, we focused on its two aspects, athletics and training. In conclusion, we proposed to combine individual training like Japanese shugyo influenced mainly by Zen philosophy with athletics developed in the West since the time of the (...) Greeks. When these are separated, the self of an athlete is still incomplete, and it is hard to attain genuine excellence or achievement. An athlete in such a separate state ofmind possibly ends up using irrational force or power when relying on individual training. On the other hand, an athlete who focuses only on competitions will have a strong inclination to be affected by the media and commercialism, while having chances to be approved by others. It is hence essential to combine the two approaches. If we redefine playing sports as the phenomenon that comprehends both our self-reflection and our encounters with others, it will serve as an occasion of great significance for people living in today’s world. (shrink)

「人と天地との一体化」とは何か。儒学の「天人合一」説を独自の立論を通して再定義した伊藤仁斎の思想に焦点を当て、その思想的意義を問い直す。仁斎学の思想体系を平易明白に解説した入門書。.

Traditionally, the genealogy of Edo Confucianism, that is, Confucianism reinterpreted and reconstructed in the Tokugawa period, has been classified into the Chu-Hsi, Wang Yang-ming, Ancient, and Eclectic schools. These classifications are based on the most representative Confucian theories in the Tokugawa period and are useful for understanding their genealogy. However, when we try to capture the substance of Confucian thought from the interest of “education,” it is very difficult to understand the differences of each school’s educational thought based on this (...) classification. For example, according to the above classification of Confucian theories, the Jinsai and Sorai schools are also included in the Ancient school. However, it is no exaggeration to say that both educational ideas are completely different. In this study, although both Jinsai and Sorai are classified as Ancient schools, I will clarify how their educational theories are structured and how their contents are different. This study examines the content of Confucian thought from the perspective of “education.” I hope that the discussion will open up the possibility of a more precise understanding of the “educational thought” of Edo Confucianism. (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)