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Interstitial and pseudo gaps in models of Peano Arithmetic

✍ Scribed by Ermek S. Nurkhaidarov

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 111 KB
Volume: 56
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200810045

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✦ Synopsis

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 M 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.

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