Borel complexity of families of finite equivalence relations via large cardinals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910527503990784 |
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| author | Laskowski, Michael C. Ulrich, Danielle S. |
| author_facet | Laskowski, Michael C. Ulrich, Danielle S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Borel complexity of families of finite equivalence relations via large cardinals Laskowski, Michael C. Ulrich, Danielle S. Logic 03C15, 03E15 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. |
| title | Borel complexity of families of finite equivalence relations via large cardinals |
| topic | Logic 03C15, 03E15 |
| url | https://arxiv.org/abs/2407.10370 |