In this paper, we present three main results on orthologics. Firstly, we give a sufficient condition for an orthologic to have variable separation property and show that the orthomodular logic has this property. Secondly, we show that the class of modular orthologics has an infinite descending chain. Finally we show that there exists a continuum of orthologics.

Continuing, we study the Strong Downward Löwenheim–Skolem Theorems of the stationary logic and their variations. In Fuchino et al. it has been shown that the SDLS for the ordinary stationary logic with weak second-order parameters \. This SDLS is shown to be equivalent to an internal version of the Diagonal Reflection Principle down to an internally stationary set of size \. We also consider a version of the stationary logic and show that the SDLS for this logic in internal (...) interpretation \\) for reflection down to \ is consistent under the assumption of the consistency of ZFC \ “the existence of a supercompact cardinal” and this SDLS implies that the continuum is weakly Mahlo. These three “axioms” in terms of SDLS are consequences of three instances of a strengthening of generic supercompactness which we call Laver-generic supercompactness. Existence of a Laver-generic supercompact cardinal in each of these three instances also fixes the cardinality of the continuum to be \ or \ or very large respectively. We also show that the existence of one of these generic large cardinals implies the “\” version of the corresponding forcing axiom. (shrink)

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club (...) principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets. (shrink)

It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □2 p → □3 p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □5 p → □6 p).

A Boolean algebra B is said to be openly generated if {A: A ≤rc B, |A| = ℵ0} includes a club subset of [ B]ℵ0 . We show: (V = L). For any cardinal κ there exists an L∞κ-free Boolean algebra which is not openly generated (Proposition 4.1). (MA+(σ-closed)). Every L∞ℵa -free Boolean algebra is openly generated (Theorem 4.2). The last assertion follows from a characterization of openly generated Boolean algebras under MA+(σ-closed) (Theorem 3.1). Using this characterization we also prove (...) the independence of problem 7 in Scepin [15] (Proposition 4.3 and Theorem 4.4). (shrink)

For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* which does not add any new element of Pκλ . Actually ℙ* can be chosen so that ℙ* is κ-strategically closed. However we show that such (...) ℙ* itself cannot be κ-strategically closed or even <κ-strategically closed if κ is inaccessible. (shrink)

Solovay’s random-real forcing [R.M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory , Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428] is the standard way of producing real-valued measurable cardinals. Following questions of Fremlin, by giving a new construction, we show that there are combinatorial, measure-theoretic properties of Solovay’s model that do not follow from the existence of real-valued measurability.

Under the presupposition that human time perception is distorted in intertemporal choice, this study constructs a time scale in the framework of axiomatic measurement. First, the conditions (homogeneity of degree one or two) to identify the form of a time scale are proposed so that one can determine whether the hyperbolic or exponential is a more suitable function for modeling people’s discounting. Homogeneity of degree one implies that subjective time delay is measured by a power scale and its discount function (...) becomes a power-exponential type, whereas homogeneity of degree two implies that subjective time delay is measured by a log scale and its discount function becomes a hyperbolic type. Second, a method is shown for constructing a model that can reflect subadditive and superadditive discounting. A non-commutative and non-associative concatenation operation is provided to generate a time string consisting of subdivided durations that incorporates the effect of repeated delay with a subdivided duration. The discounting model is yielded by substituting these strings in an exponential model equipped with a generalized time scale, and the determination of subadditivity or superadditivity depends on whether the discount function value of a product by the non-commutative and non-associative operation is, respectively, smaller or greater than that of a product by an operation of the usual extensive structure. (shrink)

哲学というととかく難しく分かりにくいように思われがちだが、哲学者にはまずはじめにイメージがあり、術語による概念化はそのあとのことだと著者は言う。さまざまな哲学者が差し出した寓意や比喩を蒐集し、それらを もとにイメージの系譜学とでもいうべきものを作ろうとしたのが本書である。プラトンからヘーゲルまでの哲学の歴史を徹底的に噛み砕き、しかも原典に忠実に解説している。この以上分かりやすい哲学史の概説書は他にな い。.

We study L∞κ-freeness in the variety of Boolean algebras. It is shown that some of the theorems on L∞κ-free algebras which are known to hold in varieties such as groups, abelian groups etc. are also true for Boolean algebras. But we also investigate properties such as the ccc of L∞κ-free Boolean algebras which have no counterpart in the varieties above.

This note concerns the model theoretic properties of logics extending the first-order logic with monadic second-order variables equipped with the stationarity quantifier. The eight variations of the strong downward Löwenheim–Skolem Theorem down to <ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<\aleph _2$$\end{document} for this logic with the interpretation of second-order variables as countable subsets of the structures are classified into four principles. The strongest of these four is shown to be equivalent to the conjunction of CH and the (...) Diagonal Reflection Principle for internally clubness of S. Cox. We show that a further strengthening of this SDLS and its variations follow from the Game Reflection Principle of B. König and its generalizations. (shrink)

The measurement of pain depends upon subjective reports, but we know very little about how research subjects or pain patients produce self-reported judgments. Representationalist assumptions dominate the field of pain research and lead to the critical conjecture that the person in pain examines the contents of consciousness before making a report about the sensory or affective magnitude of pain experience as well as about its nature. Most studies to date have investigated what Fechner termed “outer psychophysics”: the relationship between characteristics (...) of an external stimulus and the magnitude and nature of pain experience. In contrast, Fechner originally envisioned that “inner psychophysics” should investigate the relationship between physiological states and subjective experience. Despite the lack of established research tradition, inner psychophysics has a potential utility in elucidating underlying mechanisms for the production of phenomenal self-report. We illustrate this, using causal modeling analyses of the accuracy of self-reported pain ratings from our laboratory. We submit that the results are inconsistent with representationalist assumptions. Converging trends from several domains of consciousness studies seem to suggest that we need to abandon the unquestioned doctrine of representationalism and search for a more viable framework for understanding the generation of subjective self-report. (shrink)

Based on an empirical illustration of Onta pottery and more broadly a discussion of the Japanese Mingei movement, we study the intimacy between craft work, ethics and time. We conceptualize craft work through the temporal structure of tradition, to which we find three aspects: generational rhythms of making; cycles of use and re-use amongst consumers and a commitment to historically and naturally attuned communities. We argue these temporal structures of tradition in craftwork are animated by two contrasting but co-existing ideas (...) of the good: the moral and the ethical. By developing the work of Elizabeth Grosz, we conceptualize this distinction between moral and ethical as a temporal phenomenon, specifically in differing relations to ideas of the future. Moral aspects of craft work understand the future as a progression from past, whether in preserving practices and norms, or improving upon them in relation to ideals. Ethical aspects understand the future as inherently open to chance and divergence, valuing difference, accident and the possibilities for creativity these entail. Empirically, we show evidence of both aspects in the case of Mingei—a organized movement dedicated to preserving and promoting traditional Japanese craft work. We contribute to studies of craft work by revealing and classifying its temporal aspects. We contribute to studies in business ethics by conceptualising a generative distinction between morals and ethics configured through differing understandings of time. (shrink)

We prove that the automorphism group ofP(ω)/fin remains simple if ℵ2 Cohen reals are added to a model of ZFC+CH.

During 1980–90, Japan's annual real GDP growth rate was 4.6%, but which declined to 1.2% in the 1990s. While the drop in itself is a problem, at the same time it exacerbated many other problems, namely inequality, budget deficits, and the increasing burden of an aging society.

First published in 1928, this book discusses 'the groundwork and skeleton of the common intellectual life of the people' of Japan.

This paper explores lexicographically additive representations of multi-attribute preferences on finite sets. Lexicographic additivity combines a lexicographic feature with local value tradeoffs. Tradeoff structures are governed by either transitive or nontransitive additive conjoint measurement. Alternatives are locally traded off when they are close enough within threshold associated with a dominant subset of attributes.

Given a belief function ? on the set of all subsets of prizes, how should ? values be understood as a decision alternative? This paper presents and characterizes an induced-measure interpretation of belief functions.

Japanese prefer odd numbers, whereas Westerners emphasize even numbers, an observation that is clear from the distribution of number-related words in Japanese and English dictionaries. In this article, the author explains why these two cultures differ by surveying the history of numbers, including yin-yang thought from ancient China, ancient Greek philosophy, and modern European mathematics. The author also mentions that oddness and evenness are only mathematical concepts, but understanding the cultures and histories of individual countries contributes to world peace.