Internality and interpretable automorphism groups in simple theories
type: Item
instance of: scholarly article
title: Internality and interpretable automorphism groups in simple theories
zbMATH Open document ID: 1060.03054
author: Ziv Shami
published in: Annals of Pure and Applied Logic
publication date: 2004-11-22T00:00:00Z
review text: The paper investigates some possible partial extensions of the binding group theorem from stable to simple theories. For \(T\) a simple theory, \({\mathcal Q}\) an \(\emptyset\)-invariant subset of the monster model \({\mathcal C}\) of \(T\) and \(p\) a \({\mathcal Q}\)-internal type over \(\emptyset\), the automorphism group \(G = \Aut(p({\mathcal C})/{\mathcal Q})\) is considered, a ``small'' normal subgroup \(G_0^+\) is introduced, and it is shown that \(G_0^+\) is of finite exponent and that the quotient group \(G/G_0^+\) is interpretable in an invariant way. Further results are proved under stronger assumptions on \({\mathcal Q}\) and \(p\). For instance, it is shown that, if \(p\) satisfies some suitable internality or multiplicity 1 conditions and \({\mathcal Q}\) is pseudo-open, then \(G\) is type-definable.
Mathematics Subject Classification ID: 03C45
zbMATH DE Number: 2117329
zbMATH Keywords: internal type
zbMATH Keywords: automorphism group
zbMATH Keywords: simple theory
reviewed by: Carlo Toffalori
MaRDI profile type: Publication
full work available at URL: j.apal.2003.12.004
OpenAlex ID: W1996970122
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DOI: 10.1016/J.APAL.2003.12.004
description: scientific article; zbMATH DE number 2117329