English

Measures on perfect e-free PAC fields

Logic 2022-02-09 v1

Abstract

We construct measures on definable sets in ee-free perfect PAC fields, as well as on perfect PAC fields whose absolute Galois groups are free pro-pp 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\omega-free PAC fields via ultralimit measures.

Cite

@article{arxiv.2202.03500,
  title  = {Measures on perfect e-free PAC fields},
  author = {Zoé Chatzidakis and Nicholas Ramsey},
  journal= {arXiv preprint arXiv:2202.03500},
  year   = {2022}
}
R2 v1 2026-06-24T09:25:02.516Z