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May 2019 Tame Expansions of ω-Stable Theories and Definable Groups
Haydar Göral
Notre Dame J. Formal Logic 60(2): 161-194 (May 2019). DOI: 10.1215/00294527-2019-0003

Abstract

We study groups definable in tame expansions of ω-stable theories. Assuming several tameness conditions, we obtain structural theorems for groups definable and interpretable in these expansions. As our main example, by characterizing independence in the pair (K,G), where K is an algebraically closed field and G is a multiplicative subgroup of K× with the Mann property, we show that the pair (K,G) satisfies the assumptions. In particular, this provides a characterization of definable and interpretable groups in (K,G) in terms of algebraic groups in K and interpretable groups in G. Furthermore, we compute the Morley rank and the U-rank in (K,G) and both ranks agree.

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Haydar Göral. "Tame Expansions of ω-Stable Theories and Definable Groups." Notre Dame J. Formal Logic 60 (2) 161 - 194, May 2019. https://doi.org/10.1215/00294527-2019-0003

Information

Received: 11 September 2015; Accepted: 24 December 2016; Published: May 2019
First available in Project Euclid: 25 April 2019

zbMATH: 07096535
MathSciNet: MR3952230
Digital Object Identifier: 10.1215/00294527-2019-0003

Subjects:
Primary: 03C45

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 2 • May 2019
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