Borel complexity of families of finite equivalence relations via large cardinals

2024/07/15 by Laskowski, Michael C., Ulrich, Danielle S.
#03C15 #03E15 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2407.10370

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 \em forbidding nested sequences which implies a tight upper bound on Borel complexity, and \em 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.

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