G-Compactness and Groups

Details G-Compactness and Groups G-Compactness and Groups

2007-07-16

arxiv.org/abs/0707.2400v2

Archive for Mathematical Logic, 47 (2008), no. 5, 479--501

Mathematics

Logic

18 pages

Scientific paper

10.1007/s00153-008-0092-4

Lascar described E_KP as a composition of E_L and the topological closure of EL. 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_0 consisting of M and X as two sorts, where X is an affine copy of G and in M_0 we have the structure of M and the action of G on X. We prove that the Lascar group of M_0 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_0. This example may yield new examples of non-G-compact theories.

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