Submission date: 21 July 2018

Abstract:

We study definable groups in dense/codense expansions of geometric theories. We show that under some tame assumptions, definably amenable groups definable in the old language remain amenable in the expansion. Under the same assumptions, we show that the connected component in the expansion agrees with the connected component in the original language. We also analyze imaginaries in the expansion when the underlying theory has disintegrated algebraic closure.

Mathematics Subject Classification: 03C45, 03C64

Keywords and phrases: unary predicate expansions, definable groups, amenable groups, Mann property, imaginaries

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