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arXiv · 2407.10370

Borel complexity of families of finite equivalence relations via large cardinals

Michael C. Laskowski·Danielle S. Ulrich
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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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Michael C. Laskowski, Danielle S. Ulrich. 2024-07-15. Borel complexity of families of finite equivalence relations via large cardinals. https://arxiv.org/abs/2407.10370

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