On two questions concerning the automorphism groups of countable recursively saturated models of PA
type: Item
instance of: scholarly article
title: On two questions concerning the automorphism groups of countable recursively saturated models of PA
zbMATH Open document ID: 0873.03037
author: Roman Kossak
author: Nicholas Bamber
published in: Archive for Mathematical Logic
publication date: 1997-10-26T00:00:00Z
review text: The paper is devoted to some problems concerning the automorphism groups of models of Peano arithmetic PA. In particular, it is proved that (1) the automorphism group of a countable recursively saturated model of PA is not divisible and (2) every countably recursively saturated model has a strong initial segment whose setwise stabilizer is not maximal. Definability in structures of the form \((M,I)\), where \(M\) is a model of PA an \(I\) is an initial segment of \(M\), is also considered. A generalization of a result of Kanovej is given.
Mathematics Subject Classification ID: 03C62
Mathematics Subject Classification ID: 03H15
Mathematics Subject Classification ID: 03C50
zbMATH DE Number: 1006569
zbMATH Keywords: definability
zbMATH Keywords: automorphism groups
zbMATH Keywords: models of Peano arithmetic
zbMATH Keywords: recursively saturated model
zbMATH Keywords: strong initial segment
zbMATH Keywords: setwise stabilizer
reviewed by: Roman Murawski
MaRDI profile type: Publication
full work available at URL: s001530050056
OpenAlex ID: W2029404498
DOI: 10.1007/S001530050056
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description: scientific article; zbMATH DE number 1006569