Submission date: 15 July 2024

Abstract:

We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an ω-Erdos cardinal, we determine which of these theories are Borel complete. We develop machinery, including forbidding nested sequences which implies a tight upper bound on Borel complexity, and admitting cross-cutting absolutely indiscernible sets which in our context implies Borel completeness. In the Appendix we classify the reducts of theories of refining equivalence relations, possibly with infinite splitting.

Mathematics Subject Classification: 03C15, 03E15

Keywords and phrases:

Full text arXiv 2407.10370: pdf, ps.