G-compactness and groups

Archive for Mathematical Logic 47 (5):479-501 (2008)
Abstract
Lascar described E KP as a composition of E L and the topological closure of E L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G L . We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories
Keywords Strong types   G-compactness  Automorphisms groups
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DOI 10.1007/s00153-008-0092-4
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References found in this work BETA

Hyperimaginaries and Automorphism Groups.D. Lascar & A. Pillay - 2001 - Journal of Symbolic Logic 66 (1):127-143.
Galois Groups of First Order Theories.E. Casanovas, D. Lascar, A. Pillay & M. Ziegler - 2001 - Journal of Mathematical Logic 1 (02):305-319.
On Bounded Type-Definable Equivalence Relations.Ludomir Newelski & Krzysztof Krupi?Ski - 2002 - Notre Dame Journal of Formal Logic 43 (4):231-242.

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Citations of this work BETA

Connected Components of Definable Groups, and o-Minimality II.Annalisa Conversano & Anand Pillay - 2015 - Annals of Pure and Applied Logic 166 (7-8):836-849.

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