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  1. The Generic Filter Property in Nonstandard Analysis.Mauro Di Nasso - 2001 - Annals of Pure and Applied Logic 111 (1-2):23-37.
    In this paper two new combinatorial principles in nonstandard analysis are isolated and applications are given. The second principle provides an equivalent formulation of Henson's isomorphism property.
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  • Maharam Spectra of Loeb Spaces.Renling Jin & H. Jerome Keisler - 2000 - Journal of Symbolic Logic 65 (2):550-566.
    We characterize Maharam spectra of Loeb probability spaces and give some applications of the results.
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  • Compactness of Loeb Spaces.Renling Jin & Saharon Shelah - 1998 - Journal of Symbolic Logic 63 (4):1371-1392.
    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].
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  • Distinguishing Three Strong Saturation Properties in Nonstandard Analysis.Renling Jin - 1999 - Annals of Pure and Applied Logic 98 (1-3):157-171.
    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 (...)
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  • Isomorphism Property in Nonstandard Extensions of theZFC Universe.Vladimir Kanovei & Michael Reeken - 1997 - Annals of Pure and Applied Logic 88 (1):1-25.
    We study models of HST . This theory admits an adequate formulation of the isomorphism propertyIP, which postulates that any two elementarily equivalent internally presented structures of a well-orderable language are isomorphic. We prove that IP is independent of HST and consistent with HST.
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  • Game Sentences and Ultrapowers.Renling Jin & H. Jerome Keisler - 1993 - Annals of Pure and Applied Logic 60 (3):261-274.
    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 (...)
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  • Combinatorial Principles in Nonstandard Analysis.Mauro Di Nasso & Karel Hrbacek - 2003 - Annals of Pure and Applied Logic 119 (1-3):265-293.
    We study combinatorial principles related to the isomorphism property and the special model axiom in nonstandard analysis.
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  • Special Model Axiom in Nonstandard Set Theory.Vladimir Kanovei & Michael Reeken - 1999 - Mathematical Logic Quarterly 45 (3):371-384.
    We demonstrate that the special model axiom SMA of Ross admits a natural formalization in Kawai's nonstandard set theory KST but is independent of KST. As an application of our methods to classical model theory, we present a short proof of the consistency of the existence of a k+ like k-saturated model of PA for a given cardinal k.
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