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September 2010 Definability of groups in ℵ₀-stable metric structures
Itaï Ben Yaacov
J. Symbolic Logic 75(3): 817-840 (September 2010). DOI: 10.2178/jsl/1278682202

Abstract

We prove that in a continuous ℵ₀-stable theory every type-definable group is definable. The two main ingredients in the proof are:

1. Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and

2. Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.

Citation

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Itaï Ben Yaacov. "Definability of groups in ℵ₀-stable metric structures." J. Symbolic Logic 75 (3) 817 - 840, September 2010. https://doi.org/10.2178/jsl/1278682202

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1205.03047
MathSciNet: MR2723769
Digital Object Identifier: 10.2178/jsl/1278682202

Subjects:
Primary: 03C45, 03C90

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 3 • September 2010
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