Interstitial and pseudo gaps in models of Peano Arithmetic

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Abstract

In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic a is a maximal subgroup of Aut(M) if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a ∈ Ω, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational.

Original languageEnglish (US)
Pages (from-to)198-204
Number of pages7
JournalMathematical Logic Quarterly
Volume56
Issue number2
DOIs
StatePublished - Mar 1 2010

All Science Journal Classification (ASJC) codes

  • Logic

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