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G-compactness and groups

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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.

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Authors and Affiliations

  1. Instytut Matematyczny, Uniwersytetu Wrocławskiego, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Jakub Gismatullin & Ludomir Newelski

Authors
  1. Jakub Gismatullin
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  2. Ludomir Newelski
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Corresponding author

Correspondence to Jakub Gismatullin.

Additional information

The first author is supported by the Polish Goverment grant N N201 384134. The second author is supported by the Polish Goverment grant N201 032 32/2231.

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Gismatullin, J., Newelski, L. G-compactness and groups. Arch. Math. Logic 47, 479–501 (2008). https://doi.org/10.1007/s00153-008-0092-4

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  • DOI: https://doi.org/10.1007/s00153-008-0092-4

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