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Type-definable and invariant groups in o-minimal structures

Published online by Cambridge University Press:  12 March 2014

Jana Maříková
Jana Maříková*
Affiliation:
Department of Mathematics, University of Illinois, Urbana-Champaign, 257 Altgeld Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: marikova@math.uiuc.edu
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Abstract

Let M be a big o-minimal structure and G a type-definable group in Mn. We show that G is a type-definable subset of a definable manifold in Mn that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for the wider class of so-called invariant groups: each invariant group G in Mn has a unique topology making it a topological group and inducing the same topology on a large invariant subset of the group as Mn.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 67 - 80
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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