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Preprint Number 1436

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1436. Pantelis E. Eleftheriou
Large groups are o-minimal

Submission date: 29 May 2018


Let N be an expansion of an o-minimal structure M such that every open definable set is definable in M. Assume that N admits a dimension function compatible with M. Among all definable groups, we characterize those definable in M as the ones that have maximal dimension; namely, their dimension equals the dimension of their topological closure. Our setting includes all known tame expansions N=(M,P), where P is a dense subset of M. As an application, we obtain that if P is independent, then every definable group is already definable in M.

Mathematics Subject Classification: 03C64

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Full text arXiv 1805.11500: pdf, ps.

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