Borel complexity of families of finite equivalence relations via large cardinals
Abstract
Abstract We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an $$\omega $$ ω -Erdős 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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Archive for Mathematical Logic
- Volume
- 65
- Issue
- 4
- Pages
- 477–508
- Publication date
- 26 February 2026
- Language
- EN