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)

在中國伊斯蘭教研究中，有“回族四大著作家”（王岱輿、馬注、劉智、馬複初）的說法。馬注思想之所以值得重視和研究，完全與他出生於回族世家，自幼受儒學教育從而在融合伊斯蘭與儒家思想方面，做出了重要貢獻。他的 《清真指南》堪稱伊斯蘭教中國化方面的傑出代表作。當前，世界範圍內伊斯蘭教的賽萊菲耶極其活躍。它在國際政治領域，已經產生了可見的危害；它在思想、文化、宗教領域的流傳，人們同樣不應低估它的嚴重影響。.

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.

本书是作者晚年在老朋友的建议下撰写的回忆录，内容涉及与他交往密切的老朋友、个人经历和治学活动，以及生活情趣等等。.

In a recent Target Article Naomi Scheinerman (2023a) has offered an important and compelling call to institutionalize popular participation for heritable genome engineering through the inclusion of...

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)

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.

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)

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)

volume 1. Yi tong ; Zhou yi jiang zuo -- volume 2. Zhou yi quan jie -- volume 3. "Zhou yi, Xi ci zhuan" xin bian xiang jie ; "Shang shu, Yu xia shu" xin jie -- volume 4. Zhongguo nu li she hui de ji ge wen ti ; Lun jing tian zhi du ; Zhongguo nu li she hui shi -- volume 5. Kongzi xin zhuan -- volume 6. Jing xue gai lun ; Xian Qin si xiang shi (...) ; Xian Qin si xiang shi zhuan ti jiang shou ti gang -- volume 7. Lun wen Jing xue bian, Shi xue bian -- volume 8. Lun wen Shi xue bian, Zi xue bian -- volume 9. Lun wen Zi xue bian, Xu ba bian, Za zhu bian ; Zi zhuan -- volume 10. Fu lu. (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)

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)