Submission date: 24 January 2022

Abstract:

We generalize the notions of definable amenability and extreme definable amenability to continuous structures and show that the stable and ultracompact groups are definable amenable. In addition, we characterize both notions in terms of fixed-point properties. We prove that, for dependent theories, definable amenability is equivalent to the existence of a good S1 ideal. Finally, we show the randomizations of first-order definable amenable groups are extreme definably amenable.

Mathematics Subject Classification: 03C66 03C45 43A07

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Full text arXiv 2201.09971: pdf, ps.