Submission date: 7 February 2022

Abstract:

We construct measures on definable sets in e-free perfect PAC fields, as well as on perfect PAC fields whose absolute Galois groups are free pro-p of finite rank. We deduce the definable amenability of all groups definable in such fields. As a corollary, we additionally prove the definable amenability of all groups definable in perfect ω-free PAC fields via ultralimit measures.

Mathematics Subject Classification:

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Full text arXiv 2202.03500: pdf, ps.