Definably amenable groups in Continuous logic

Juan Felipe Carmona; Alf Onshuus

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arXiv · 2201.09971

Definably amenable groups in Continuous logic

Juan Felipe Carmona·Alf Onshuus

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Abstract

We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both notions using fixed-point properties. We show that stable and ultracompact groups are definably amenable and prove that, for groups definable in dependent theories, definable amenability is equivalent to the existence of an f-generic type. Finally, we show the randomizations of first-order definably amenable groups are extremely definably amenable.

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BibTeX RIS

Juan Felipe Carmona, Alf Onshuus. 2022-01-24. Definably amenable groups in Continuous logic. https://arxiv.org/abs/2201.09971

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