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Borel Complexity of Families of Finite Equivalence Relations via Large Cardinals by Laskowski, Michael C.; Ulrich, Danielle S. is a scholarly article available to read on EtoBox.

What is Borel Complexity of Families of Finite Equivalence Relations via Large Cardinals about?

We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an $\omega$-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.

Author

Laskowski, Michael C.; Ulrich, Danielle S.

Published

2024

Language

EN