On expandability of models of peano arithmetic to models of the alternative set theory

Journal of Symbolic Logic 57 (2):452-460 (1992)
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Abstract

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 whether the intersection of all β-expansions of a β-expandable model M is the set RA(M, ω)--the ramified analytical hierarchy over (M, ω). The results are based on forcing constructions

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Elementary Induction on Abstract Structures.Wayne Richter - 1979 - Journal of Symbolic Logic 44 (1):124-125.
A Note on Real Subsets of A Recursively Saturated Model.Athanassios Tzouvaras - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (13-16):207-216.
A Note on Real Subsets of A Recursively Saturated Model.Athanassios Tzouvaras - 1991 - Mathematical Logic Quarterly 37 (13‐16):207-216.

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