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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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  • The Strength of the Isomorphism Property.Renling Jin & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):292-301.
    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.
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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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  • 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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