Recent insights reveal the significant role of TRPV3 in warmth sensation. A novel finding elucidated how thermosensation is affected by TRPV3 membrane abundance that is modulated by the transmembrane protein TMEM79. TRPV3 is a warmth‐sensitive ion channel predominantly expressed in epithelial cells, particularly skin keratinocytes. Multiple studies investigated the roles of TRPV3 in cutaneous physiology and pathophysiology. TRPV3 activation by innocuous warm temperatures in keratinocytes highlights its significance in temperature sensation, but whether TRPV3 directly contributes to warmth sensations in vivo (...) remains controversial. This review explores the electrophysiological and structural properties of TRPV3 and how modulators affect its intricate regulatory mechanisms. Moreover, we discuss the multifaceted involvement of TRPV3 in skin physiology and pathology, including barrier formation, hair growth, inflammation, and itching. Finally, we examine the potential of TRPV3 as a therapeutic target for skin diseases and highlight its diverse role in maintaining skin homeostasis. (shrink)

Within a weak subsystem of second-order arithmetic , that is -conservative over , we reformulate Kreisel's proof of the Second Incompleteness Theorem and Boolos' proof of the First Incompleteness Theorem.

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)

In the past decade, a growing number of authors, notably Thomas Pogge, have maintained that citizens in economically advanced societies are responsible for extreme and extensive poverty in the developing world. Iris Marion Young proposed the social connection model of responsibility, which asserts that these citizens participate in networks that give rise to global structural injustices. While Pogge’s argument for the existence of citizens’ responsibility has been the subject of widespread debate, few efforts have been made to scrutinise the solidity (...) of Young’s perspective. To plug this gap in the literature, this paper assesses the pertinence of Young’s view. A more traditional view than those of Pogge and Young considers poverty as indicating a lack of respect for the human rights of those living in less-developed countries. Rights theorists of global justice, however, have paid scant attention to philosophical observations concerning redistribution within the borders of a society. To remedy this shortcoming, this paper endeavours to develop the theory that citizens in affluent societies bear a duty correlative to the subsistence right of the global needy, by exploring sufficientarianism, which is one of the primary views on domestic redistribution. To begin with, I make a distinction between the responsibility-based theory and the right-based theory of global justice. This is followed by a close examination of Young’s social connection model as a significant version of the former position. I then offer a right-based argument that invokes the sufficientarian idea of the human right to live above the threshold of safe and healthy subsistence. (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)

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)

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 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.

In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one (...) that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with MON determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers. (shrink)

We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” and “multilateral”. In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

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.

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 systematically study the interrelations between all possible variations of $\Delta ^0_1$ variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis.

On sait que Platon fait grand cas des êtres intelligibles en instaurant la théorie des Idées. Mais il n’est pas approprié de le considérer comme penseur qui néglige le rôle de l’apparence sensible. Ce philosophe demeure très sensible à la modalité par laquelle les phénomènes apparaissent dans le champ de notreperception. En distinguant deux types d’apparence : image et simulacre, il donne à l’image le rôle d’intermédiaire actif entre le sensible et l’intelligible. L’examen des modalités des actions humaines qui reçoivent (...) et créent des images, nous aide à voir comment Platon intègre la fonction des images dans la structure de sa philosophie. La réception et la création des images sont étroitement reliées et synthétisées pour former le système original de Platon, système dans lequel le fondement de la théorie des Idées relève d’un certain dynamisme de l’action humaine. Dans la recherche relative à la modalité de réception et de création des images, je porte mon attention sur l’usage platonicien du terme tupos qui exprime le principe de la conformité de l’image et de son modèle.Notamment dans la théorie de la formation des futurs gardiens de la cité idéale, le tupos fonctionne, comme un principe qui réglemente et oriente à plusieurs niveaux les activités de la mimèsis et de la poièsis qui portent sur les images. La réflexion sur cette fonction conductrice. (shrink)

Interleukin 5 (IL‐5) is a kind of peptide hormone released from T lymphocytes of mammals infected with microorganisms or parasites. It is an acidic glycoprotein with a molecular mass of 40 to 50 kDa that consists of a homodimer of polypeptides. It controls hematopoiesis so that it increases natural immunity. In the mouse, IL‐5 acts on committed B cells to induce differentiation into Ig‐producing cells and on common progenitors for CD5+ pre‐B cells and CD5+ macrophages to support their survival. The (...) antibodies secreted by CD5+ B cells seem to be responsible for the primary protection against the infection with microorganisms or parasites. It also supports the growth and/or differentiation of eosinophil precursor and mature eosinophils, which can be effective for the removal of parasites in combination with the antibodies against them. Murine IL‐5 receptor (IL‐5R) consists of two different polypeptide chains; αL chain and β chain. The IL‐5R α chain is 60 kDa protein that binds IL‐5 with low affinity. The IL‐5R β chain is a 130 kDa protein which does not bind IL‐5 by itself but is necessary to form the high affinity IL‐5R. The β chain was identified by using one of the anti‐IL‐5R mAb and anti‐IL‐3R mAb as the IL‐3R homologue. This β chain is also used as the β chain of GM‐CSF receptor. This fact suggests that there is a common signaling mechanism among these cytokines and efficient cooperation among them. At the same time, these findings may explain the overlapping role of these cytokines in the development of granulocytes. (shrink)

Savant syndrome and prime numbers Oliver Sacks reported that a pair of autistic twins had extraordinary number abilities and that they spontaneously generated huge prime numbers. Such abilities could contradict our understanding of human abilities. Sacks' report attracted widespread attention, and several researchers speculated theoretically. Unfortunately, most of the explanations in the literature are wrong. Here a correct explanation on prime number identification is provided. Fermat's little theorem is implemented in spreadsheet. Also, twenty years after the report, questionable aspects were (...) found in it. Extreme abilities became dubious. One possibility for the less extreme abilities is incomplete trial division. (shrink)

We give a proof of Gödel's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model-theoretically.

By using a provability predicate of PA, we define ThmPA(M) as the set of theorems of PA in a modelMof PA. We say a modelMof PA is (1) illusory if ThmPA(M) ⊈ ThmPA(ℕ), (2) heterodox if ThmPA(M) ⊈ TA, (3) sane ifM⊨ ConPA, and insane if it is not sane, (4) maximally sane if it is sane and ThmPA(M) ⊆ ThmPA(N) implies ThmPA(M) = ThmPA(N) for every sane modelNof PA. We firstly show thatMis heterodox if and only if it is (...) illusory, and that ThmPA(M) ∩ TA ≠ ThmPA(ℕ) for any illusory modelM. Then we show that there exists a maximally sane model, every maximally sane model satisfies ¬ConPA+ConPA, and there exists a sane model of ¬ConPA+ConPAwhich is not maximally sane. We define that an insane model is (5) illusory by nature if its every initial segment being a nonstandard model of PA is illusory, and (6) going insane suddenly if its every initial segment being a sane model of PA is not illusory. We show that there exists a model of PA which is illusory by nature, and we prove the existence of a model of PA which is going insane suddenly. (shrink)

We identify bar recursion on moduli of continuity as a fundamental notion of constructive mathematics. We show that continuous functions from the Baire space \ to the natural numbers \ which have moduli of continuity with bar recursors are exactly those functions induced by Brouwer operations. The connection between Brouwer operations and bar induction allows us to formulate several continuity principles on the Baire space stated in terms of bar recursion on continuous moduli which naturally characterise some variants of bar (...) induction. These principles state that a certain kind of continuous function from \ to \ admits a modulus of continuity with a bar recursor. The results for the Baire space are recast in the setting of the Cantor space \ using the notion of fan recursor, a bar recursor for binary trees. This yields characterisations of uniformly continuous functions on the Cantor space and fan theorem in terms of fan recursors. The results for the Cantor space hold over the extensional version of intuitionistic arithmetic in all finite types ), and those for the Baire space hold over \ extended with the type for Brouwer operations. Our work places Spector’s bar recursion in a proper context of Brouwer’s intuitionistic mathematics and clarifies the connection between bar recursion and bar induction. (shrink)

没後20年、いま必要な歴史に裏打ちされた予見力、現実政治に提言する率直さ、道義性と理想主義。.