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  1. On Expandability of Models of Peano Arithmetic to Models of the Alternative Set Theory.Athanassios Tzouvaras - 1992 - Journal of Symbolic Logic 57 (2):452-460.
    We give a sufficient condition for a countable model M of PA to be expandable to an ω-model of AST with absolute Ω-orderings. The condition is in terms of saturation schemes or, equivalently, in terms of the ability of the model to code sequences which have some kind of definition in (M, ω). We also show that a weaker scheme of saturation leads to the existence of wellorderings of the model with nice properties. Finally, we answer affirmatively the question of (...)
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  • Nonstandard Definability.Stuart T. Smith - 1989 - Annals of Pure and Applied Logic 42 (1):21-43.
    We investigate the notion of definability with respect to a full satisfaction class σ for a model M of Peano arithmetic. It is shown that the σ-definable subsets of M always include a class which provides a satisfaction definition for standard formulas. Such a class is necessarily proper, therefore there exist recursively saturated models with no full satisfaction classes. Nonstandard extensions of overspill and recursive saturation are utilized in developing a criterion for nonstandard definability. Finally, these techniques yield some information (...)
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  • Automorphism Groups of Countable Arithmetically Saturated Models of Peano Arithmetic.James H. Schmerl - 2015 - Journal of Symbolic Logic 80 (4):1411-1434.
  • Models with the Ω-Property.Roman Kossak - 1989 - Journal of Symbolic Logic 54 (1):177-189.
    A model M of PA has the omega-property if it has a subset of order type omega that is coded in an elementary end extension of M. All countable recursively saturated models have the omega-property, but there are also models with the omega-property that are not recursively saturated. The papers is devoted to the study of structural properties of such models.
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  • Meager Sets on the Hyperfinite Time Line.H. Jerome Keisler & Steven C. Leth - 1991 - Journal of Symbolic Logic 56 (1):71-102.
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  • Remarks on Weak Notions of Saturation in Models of Peano Arithmetic.Matt Kaufmann & James H. Schmerl - 1987 - Journal of Symbolic Logic 52 (1):129-148.
  • Set Theoretical Analogues of the Barwise-Schlipf Theorem.Ali Enayat - 2022 - Annals of Pure and Applied Logic 173 (9):103158.