Nonstandard definability

Stuart T. Smith

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

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 concerning the extendibility of full satisfaction classes from one model to another.

Original languageEnglish
Pages (from-to)21-43
Number of pages23
JournalAnnals of Pure and Applied Logic
Volume42
Issue number1
DOIs
StatePublished - 28 Mar 1989

ASJC Scopus subject areas

  • Logic

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