Let U be an initial segment of $^*{\mathbb N}$ closed under addition (such U is called a cut) with uncountable cofinality and A be a subset of U, which is the intersection of U and an internal subset of $^*{\mathbb N}$ . Suppose A has lower U-density α strictly between 0 and 3/5. We show that either there exists a standard real $\epsilon$ > 0 and there are sufficiently large x in A such that | (A+A) ∩ [0, 2x]| > (...) (10/3+ $\epsilon$ ) | A ∩ [0, x]| or A is a large subset of an arithmetic progression of difference greater than 1 or A is a large subset of the union of two arithmetic progressions with the same difference greater than 2 or A is a large subset of the union of three arithmetic progressions with the same difference greater than 4. (shrink)

A construction of the real number system based on almost homomorphisms of the integers $\mathbb {Z}$ was proposed by Schanuel, Arthan, and others. We combine such a construction with the ultrapower or limit ultrapower construction to construct the hyperreals out of integers. In fact, any hyperreal field, whose universe is a set, can be obtained by such a one-step construction directly out of integers. Even the maximal (i.e., On -saturated) hyperreal number system described by Kanovei and Reeken (2004) and independently (...) by Ehrlich (2012) can be obtained in this fashion, albeit not in NBG . In NBG , it can be obtained via a one-step construction by means of a definable ultrapower (modulo a suitable definable class ultrafilter). (shrink)

This paper answers some questions of D. Ross in [R]. In § 1, we show that some consequences of the ℵ0- or ℵ1-special model axiom in [R] cannot be proved by the κ-isomorphism property for any cardinal κ. In § 2, we show that with one exception, the ℵ0-isomorphism property does imply the remaining consequences of the special model axiom in [R]. In § 3, we improve a result in [R] by showing that the κ-special model axiom is equivalent to (...) the ℵ0-special model axiom plus κ-saturation. (shrink)

A P-point ultrafilter over \(\omega \) is called an interval P-point if for every function from \(\omega \) to \(\omega \) there exists a set _A_ in this ultrafilter such that the restriction of the function to _A_ is either a constant function or an interval-to-one function. In this paper we prove the following results. (1) Interval P-points are not isomorphism invariant under \(\textsf{CH}\) or \(\textsf{MA}\). (2) We identify a cardinal invariant \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})\) such that every filter base (...) of size less than continuum can be extended to an interval P-point if and only if \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})={\mathfrak {c}}\). (3) We prove the generic existence of slow/rapid non-interval P-points and slow/rapid interval P-points which are neither quasi-selective nor weakly Ramsey under the assumption \({\mathfrak {d}}={\mathfrak {c}}\) or \(\textbf{cov}({\mathcal {B}})={\mathfrak {c}}\). (shrink)

An L-structure is called internally presented in a nonstandard universe if its base set and interpretation of every symbol in L are internal. A nonstandard universe is said to satisfy the κ-isomorphism property if for any two internally presented L-structures U and B, where L has less than κ many symbols, U is elementarily equivalent to B implies that U is isomorphic to B. In this paper we prove that the ℵ1-isomorphism property is equivalent to the ℵ0-isomorphism property plus ℵ1-saturation.

We answer a question of Blass, Di Nasso, and Forti [2, 7] by proving, assuming Continuum Hypothesis or Martin’s Axiom, that there exists a P-point which is not interval-to-one and there exists an interval-to-one P-point which is neither quasi-selective nor weakly Ramsey.

In § 1 of this paper, we characterize the isomorphism property of nonstandard universes in terms of the realization of some second-order types in model theory. In § 2, several applications are given. One of the applications answers a question of D. Ross in [this Journal, vol. 55 (1990), pp. 1233-1242] about infinite Loeb measure spaces.

Three results in [14] and one in [8] are analyzed in Sections 3–6 in order to supply examples on Loeb probability spaces, which distinguish the different strength among three generalizations of k-saturation, as well to answer some questions in Section 7 of [15]. In Section 3 we show that not every automorphism of a Loeb algebra is induced by an internal permutation, in Section 4 we show that if the 1-special model axiom is true, then every automorphism of a Loeb (...) algebra is induced by a point-automorphism, in Section 5 we show that not every measure-preserving homomorphism from a small subalgebra to a Loeb algebra is induced by an internal permutation, without assuming full-saturation, in Section 6 we show that, under some cardinality assumptions, the 1-isomorphism property does not guarantee the compactness of a Loeb space, and in Section 7 an application of the 1-special model axiom is given on the existence of ergodic transformations of a Loeb space, which partially answers Problem 2.3 of [5]. (shrink)

We prove that if is a model of size at most [kappa], λ[kappa] = λ, and a game sentence of length 2λ is true in a 2λ-saturated model ≡ , then player has a winning strategy for a related game in some ultrapower ΠD of . The moves in the new game are taken in the cartesian power λA, and the ultrafilter D over λ must be chosen after the game is played. By taking advantage of the expressive power of (...) game sentences, we obtain several applications showing the existence of ultrapowers with certain properties. In each case, it was previously known that such ultrapowers exist under the assumption of the GCH, and we get them without the GCH. Article O. (shrink)

Type two cuts, bad cuts and very bad cuts are introduced in [10] for studying the relationship between Loeb measure and U-topology of a hyperfinite time line in an ω 1 -saturated nonstandard universe. The questions concerning the existence of those cuts are asked there. In this paper we answer, fully or partially, some of those questions by showing that: (1) type two cuts exist, (2) the ℵ 1 -isomorphism property implies that bad cuts exist, but no bad cuts are (...) very bad. (shrink)

In this paper we probe the possibilities of creating a Kurepa tree in a generic extension of a ground model of CH plus no Kurepa trees by an ω1-preserving forcing notion of size at most ω1. In Section 1 we show that in the Lévy model obtained by collapsing all cardinals between ω1 and a strongly inaccessible cardinal by forcing with a countable support Lévy collapsing order, many ω1-preserving forcing notions of size at most ω1 including all ω-proper forcing notions (...) and some proper but not ω-proper forcing notions of size at most ω1 do not create Kurepa trees. In Section 2 we construct a model of CH plus no Kurepa trees, in which there is an ω-distributive Aronszajn tree such that forcing with that Aronszajn tree does create a Kurepa tree in the generic extension. At the end of the paper we ask three questions. (shrink)

Let $\omega$ be the first infinite ordinal (or the set of all natural numbers) with the usual order $<$ . In § 1 we show that, assuming the consistency of a supercompact cardinal, there may exist an ultrapower of $\omega$ , whose cardinality is (1) a singular strong limit cardinal, (2) a strongly inaccessible cardinal. This answers two questions in [1], modulo the assumption of supercompactness. In § 2 we construct several $\lambda$ -Archimedean ultrapowers of $\omega$ under some large cardinal (...) assumptions. For example, we show that, assuming the consistency of a measurable cardinal, there may exist a $\lambda$ -Archimedean ultrapower of $\omega$ for some uncountable cardinal $\lambda$ . This answers a question in [8], modulo the assumption of measurability. (shrink)

By an ω1 we mean a tree of power ω1 and height ω1. An ω1-tree is called a Kurepa tree if all its levels are countable and it has more than ω1 branches. An ω1-tree is called a Jech-Kunen tree if it has κ branches for some κ strictly between ω1 and $2^{\omega _1 }$ . In Sect. 1, we construct a model ofCH plus $2^{\omega _1 } > \omega _2$ , in which there exists a Kurepa tree with not (...) Jech-Kunen subtrees and there exists a Jech-Kunen tree with no Kurepa subtrees. This improves two results in [Ji1] by not only eliminating the large cardinal assumption for [Ji1, Theorem 2] but also handling two consistency proofs of [Ji1, Theorem 2 and Theorem 3] simultaneously. In Sect. 2, we first prove a lemma saying that anAxiom A focing of size ω1 over Silver's model will not produce a Kurepa tree in the extension, and then we apply this lemma to prove that, in the model constructed for Theorem 2 in [Ji1], there exists a Jech-Kunen tree and there are no Kurepa trees. (shrink)

This paper reports recent progress in applying nonstandard analysis to additive number theory, especially to problems involving upper Banach density.

In an ω1-saturated nonstandard universe a cut is an initial segment of the hyperintegers which is closed under addition. Keisler and Leth in [KL] introduced, for each given cut U, a corresponding U-topology on the hyperintegers by letting O be U-open if for any x ∈ O there is a y greater than all the elements in U such that the interval $\lbrack x - y, x + y\rbrack \subseteq O$ . Let U be a cut in a hyperfinite time (...) line H, which is a hyperfinite initial segment of the hyperintegers. U is called a good cut if there exists a U-meager subset of H of Loeb measure one. Otherwise U is bad. In this paper we discuss the questions of Keisler and Leth about the existence of bad cuts and related cuts. We show that assuming $\mathbf{b} > \omega_1$, every hyperfinite time line has a cut with both cofinality and coinitiality uncountable. We construct bad cuts in a nonstandard universe under ZFC. We also give two results about the existence of other kinds of cuts. (shrink)

In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In $\S1$ we prove that Loeb spaces are compact under various assumptions, and in $\S2$ we prove that Loeb spaces are not compact under various other assumptions. The results in $\S1$ and $\S2$ give a quite complete answer to a question of D. Ross in [9], [11] and [12].

By an ω1-tree we mean a tree of cardinality ω1 and height ω1. An ω1-tree is called a Kurepa tree if all its levels are countable and it has more than ω1 branches. An ω1-tree is called a Jech–Kunen tree if it has κ branches for some κ strictly between ω1 and 2ω1. A Kurepa tree is called an essential Kurepa tree if it contains no Jech–Kunen subtrees. A Jech–Kunen tree is called an essential Jech–Kunen tree if it is no (...) Kurepa subtrees. In this paper we prove that it is consistent with CH and 2ω1 #62; ω2 that there exist essential Kurepa trees and there are no essential Jech–Kunen trees, it is consistent with CH and 2ω1 #62; ω2 plus the existence of a Kurepa tree with 2ω1 branches that there exist essential Jech–Kunen trees and there are no essential Kurepa trees. In the second result we require the existence of a Kurepa tree with 2ω1 branches in order to avoid triviality. (shrink)

Answers are given to two questions concerning the existence of some sparse subsets of $\mathscr{H} = \{0, 1,..., H - 1\} \subseteq * \mathbb{N}$ , where H is a hyperfinite integer. In § 1, we answer a question of Kanovei by showing that for a given cut U in H, there exists a countably determined set $X \subseteq \mathscr{H}$ which contains exactly one element in each U-monad, if and only if U = a · N for some $a \in \mathscr{H} (...) \backslash \{0\}$ . In §2, we deal with a question of Keisler and Leth in [6]. We show that there is a cut $V \subseteq \mathscr{H}$ such that for any cut U, (i) there exists a U-discrete set $X \subseteq \mathscr{H}$ with X + X = H (mod H) provided $U \subsetneqq V$ , (ii) there does not exist any U-discrete set $X \subseteq \mathscr{H}$ with X + X = H (mod H) provided $\supsetneqq V$ . We obtain some partial results for the case U = V. (shrink)

We characterize Maharam spectra of Loeb probability spaces and give some applications of the results.

We characterize Maharam spectra of Loeb probability spaces and give some applications of the results.

In an ω1-saturated nonstandard universe a cut is an initial segment of the hyperintegers which is closed under addition. Keisler and Leth in [KL] introduced, for each given cut U, a corresponding U-topology on the hyperintegers by letting O be U-open if for any x ∈ O there is a y greater than all the elements in U such that the interval $\lbrack x - y, x + y\rbrack \subseteq O$ . Let U be a cut in a hyperfinite time (...) line H, which is a hyperfinite initial segment of the hyperintegers. A subset B of H is called a U-Lusin set in H if B is uncountable and for any Loeb-Borel U-meager subset X of H, B ∩ X is countable. Here a Loeb-Borel set is an element of the σ-algebra generated by all internal subsets of H. In this paper we answer some questions of Keisler and Leth about the existence of U-Lusin sets by proving the following facts. (1) If $U = x/\mathbb{N} = \{y \in \mathscr{H}: \forall n \in \mathbb{N}(y < x/n)\}$ for some x ∈ H, then there exists a U-Lusin set of power κ if and only if there exists a Lusin set of the reals of power κ. (2) If U ≠ x/N but the coinitiality of U is ω, then there are no U-Lusin sets if CH fails. (3) Under ZFC there exists a nonstandard universe in which U-Lusin sets exist for every cut U with uncountable cofinality and coinitiality. (4) In any ω2-saturated nonstandard universe there are no U-Lusin sets for all cuts U except U = x/N. (shrink)

In an ω1-saturated nonstandard universe a cut is an initial segment of the hyperintegers which is closed under addition. Keisler and Leth in [KL] introduced, for each given cut U, a corresponding U-topology on the hyperintegers by letting O be U-open if for any x ∈ O there is a y greater than all the elements in U such that the interval $\lbrack x - y, x + y\rbrack \subseteq O$ . Let U be a cut in a hyperfinite time (...) line H, which is a hyperfinite initial segment of the hyperintegers. The U-monad topology of H is the quotient topology of the U-topological space H modulo U. In this paper we answer a question of Keisler and Leth about the U-monad topologies by showing that when H is κ-saturated and has cardinality κ, (1) if the coinitiality of U1 is uncountable, then the U1-monad topology and the U2-monad topology are homeomorphic iff both U1 and U2 have the same coinitiality; and (2) H can produce exactly three different U-monad topologies (up to homeomorphism) for those U's with countable coinitiality. As a corollary H can produce exactly four different U-monad topologies if the cardinality of H is ω1. (shrink)

该研究简要介绍了儒家、佛教和道教在越南的起源和发展，以及它们如何通过 "文化叠加性 "来共存、互动、影响越南社会。基于文化叠加性的成本效益分析，本文进一步说明了儒家思想如何在越南社会中占主导地位，道教思想如何与儒家思想共存，以及为什么佛教影响力逐渐在越南民间消失。.

This study investigates the mechanism of how sensory experiences influence visitors’ digital engagement with a destination through establishing a strong bond and identification between a destination and tourist utilizing a two-step process. First, visitors’ sensory experiences in a destination are identified through a content analysis of online review comments posted by visitors. Afterward, the effects of those sensory experiences on visitors’ digital engagement through destination dependence and identification with that destination are examined. Findings suggest that sensory experiences are critical antecedents (...) of visitors’ bond and identification with a destination. Visitors’ positive destination-related sensory experiences increase their dependence on and identification with the destination, and this dependence and identification positively influence their digital engagement behavior on social media. (shrink)

Throughout the COVID-19 pandemic, shortages of scarce healthcare resources consistently presented significant moral and practical challenges. While the importance of vaccines as a key pharmaceutical intervention to stem pandemic scarcity was widely publicized, a sizable proportion of the population chose not to vaccinate. In response, some have defended the use of vaccination status as a criterion for the allocation of scarce medical resources. In this paper, we critically interpret this burgeoning literature, and describe a framework for thinking about vaccine-sensitive resource (...) allocation using the values of responsibility, reciprocity, and justice. Although our aim here is not to defend a single view of vaccine-sensitive resource allocation, we believe that attending critically with the diversity of arguments in favor (and against) vaccine-sensitivity reveals a number of questions that a vaccine-sensitive approach to allocation should answer in future pandemics. (shrink)

Tetsuro Watsuji's Notion of Fudo and Its Cultural Significance -- 'Self-less Openness' and Fudo: Renewed Sustainable Significance of Japanese Vernacular Architecture -- The Ecology of 'We' and Ambient Warmth: Richard Neutra's Ecological Architecture -- Dialectics between the Regional and the Trans-Regional.

This dissertation contextualizes the emergence of the Church of Light by Tadao Ando within the Japanese religio-philosophical tradition of nothingness. The idea of nothingness was revived during the first half of the twentieth-century by Kitaro Nishida with two cultural ramifications in the post-war period: a series of dialogues on the points of convergence and divergence between nothingness and the God of Christianity, and an architectural art movement called Monoha, or l'Ecole de Choses. Under the concept of "structuring emptiness," Monoha attempted (...) to restore perceptual depth where dichotomous semiotic representation is overcome through shintaisei, the co-originating corporeal fabric between the subject and object. This two-fold mapping, theological and architectural, not only illuminates the post-war cultural milieu from which Ando's church of spatial emptiness emerged, but also locates the church within the legacy of Nishida's nothingness. ;Nishida's philosophy of nothingness offers a perceptual theory of the "dialectic of self-negation" enacted by shintai, "the actively knowing body." Shintai is the agent of emptying selfhood by functioning as 'the sensational capacity to be filled by' the world. Shintai concretizes the perceptual matrix of co-emergence between the interiority of selfhood and the outside world. When its sensational capacity overflows, shintai enters into the realm of creative action to accommodate the surplus. The figure thus created is not a sign embodying subjective intentions, but constitutes the corporelly-inscribed, pre-reflective experiential datum of the world. Nishida called such a figure "the pure body of the artist," implying its apprehension not as the other in unknowable confrontation, but as the extended self. ;The dissertation examines how this notion of self-renunciatory perception through shintai opens a new hermeneutic horizon for the Church of Light. The church presents an unprecedented conjunction between emptiness, based on the reductive removal of signs, and the cross of light. This seemingly contradictory integration confronts the modern degradation of the cross into an atrophied sign of Christianity and seeks to retrieve its fully efficacious symbolic power. The emptiness contributes to the revival of a deeper communicative mode as shintai by negating the habituated perception pivoted upon the dichotomy between the deciphering subject and the semiotic elements. The perception of light, a natural thing rather than a sign, which infiltrates the cross, is a preliminary ritual to save the perception from the paradigm of the semiotic representation. Shintai, the self-emptying corporeality, resonates with and becomes penetrated by, rather than subjectivizes, the light. On this restored perceptual depth, the cross is perceived not as a sign, but as a part of the pre-reflective, ontological datum constructed and apprehended by shintai. This perceptual experience endorses the associational similarity between the pre-Christian datum predicated upon shintai as the agent of the self-renunciatory subjectivity and Christianity with its theology of the self-transcending love of kenosis. (shrink)

: In his philosophy of nothingness, Kitar Nishida illuminates the matrix of transformation of the world ‘‘from the Created to the Creating’’ (tsukuru mono kara tsukurareta mono e) through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The ‘‘Space of Transparency’’ put forth (...) by Ufan Lee, the leader of Monoha, is the principal example. This essay investigates Nishida’s notion of shintai and its influence on Lee’s theory of art. (shrink)

Studies have shown that internal whistleblowing could be utilized as an effective way to stop an organization’s unethical behaviors. This study investigates the relationship between ethical leadership and internal whistleblowing by focusing on the mediating role of employee-perceived organizational politics and the moderating role of moral courage. An analysis of data collected at three phases indicates that employee-perceived organizational politics partly mediates the relationship between ethical leadership and internal whistleblowing. Also, moral courage is found to moderate the effect of employee-perceived (...) organizational politics on internal whistleblowing and the indirect effect of ethical leadership on internal whistleblowing via employee-perceived organizational politics. Theoretical and practical implications of these results are discussed. (shrink)

According to Hobbes, individuals care about their relative standing in a way that shapes their social interactions. To model this aspect of Hobbesian psychology, this paper supposes that agents have social preferences, that is, preferences about their comparative resource holdings. Introducing uncertainty regarding the social preferences of others unleashes a process of trust-unravelling, ultimately leading to Hobbes’s ‘state of war’. This Trust-unravelling Model incorporates important features of Hobbes’s argument that past models ignore.

In his philosophy of nothingness, Kitar Nishida illuminates the matrix of transformation of the world ''from the Created to the Creating'' through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The ''Space of Transparency'' put forth by Ufan Lee, the leader of Monoha, (...) is the principal example. This essay investigates Nishida's notion of shintai and its influence on Lee's theory of art. (shrink)

Gitik and Rinot :1771–1795, 2012) proved assuming the existence of a supercompact that it is consistent to have a strong limit cardinal \ of countable cofinality such that \, there is a very good scale at \, and \ fails along some reflecting stationary subset of \\). In this paper, we force over Gitik and Rinot’s model but with a modification of Gitik–Sharon :311, 2008) diagonal Prikry forcing to get this result for \.

Fontanella :193–207, 2014) showed that if \ is an increasing sequence of supercompacts and \, then the strong tree property holds at \. Building on a proof by Neeman, we show that the strong tree property at \ is consistent with \, where \ is singular strong limit of countable cofinality.

Interpretation from the perspective of the historical development of global imbalances can be defined as the persistent global imbalances, the current scale is not balanced and financial imbalances. Historically there have been two of the largest global imbalances, which lasted until World War I nearly half the world's imbalances and since the 1990s until 2007, before the outbreak of the financial crisis of the contemporary global imbalances. The external imbalance is sustained by the national economic systems, economic policy, the global (...) economic system system system and the global political system and other important systemic factors, it has brought the global economy a great threat to sustainable development, and eventually lead to crisis. The problem of global imbalances could be regarded as persistent, sweeping imbalances of current account and financial account from the historical perspective. There were two largest global imbalances, one lasted about a half century before the First World War, and the other lasted from 1990s to the financial crisis of 2007. There were several reasons for the long term external imbalance, such as the national economy policies, global economic system, global political system and other important systemic factors which led the sustained development of global economy to the economic crisis. (shrink)

Jin Qian Dans son Discours sur la théologie naturelle des Chinois, Leibniz produit une interprétation du premier principe de la philosophie chinoise. Le présent article s’interroge sur les conditions de cette interprétation en la comparant avec la controverse entre Leibniz et Descartes par rapport à la conception de la substance. Il sera montré que, bien que Leibniz utilise un « principe herméneutique » dans son interprétation de la philosophie chinoise, ce principe n’est pas suffisant mais repose sur des conditions plus (...) fondamentales. La comparaison avec la controverse Leibniz-Descartes sur la substance permet d’identifier deux conditions majeures de l’application de ce principe herméneutique, à savoir la théorie dynamique de la substance et la conception de la théologie naturelle comme fondement de la physique, deux points sur lesquels divergent Leibniz et Descartes. (shrink)

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about (...) their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic. (shrink)

Previous literature has demonstrated that ethical leadership could predict employees’ voice behavior. However, it’s not clear how to heighten these positive effects of ethical leadership on employees’ voice behavior. Building on the AET and moral disengagement studies, we developed an integrated model. A three-wave field study investigated the relationship between ethical leadership and voice behavior by focusing on the mediating role of employees’ affective commitment and the moderating role of employees’ moral disengagement. Our matched data analysis results indicated that: employees’ (...) affective commitment partly mediated the relationship between ethical leadership and employees’ voice behavior. In addition, employees’ moral disengagement moderated the effect of ethical leadership on employees’ affective commitment and the effect of employees’ affective commitment on voice behavior, similarly, the indirect effect of ethical leadership on employees’ voice behavior via employees’ affective commitment. Theoretical and practical implications of these results are discussed. (shrink)

Food prices are a daily concern in many households’ decision-making, especially when people want to have healthier diets. Employing Bayesian Mindsponge Framework (BMF) analytics on a dataset of 710 Indonesian citizens, we found that people from wealthier households are less likely to have concerns about food prices. However, the degree of health considerations in food consumption was found to moderate against the above association. In other words, people of higher income-based social classes may worry more about food prices if they (...) care more about the health impacts of their food choices. These findings provide more insights for policymakers on the psychological aspects of promoting the balance between finance and health in food consumption. (shrink)