G-Compactness and Groups
Logic
2009-03-07 v2 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.0707.2400,
title = {G-Compactness and Groups},
author = {Jakub Gismatullin and Ludomir Newelski},
journal= {arXiv preprint arXiv:0707.2400},
year = {2009}
}
Comments
18 pages