Characterizing Borel Isomorphism Among Some Weakly Minimal Trivial Theories (2409.13134v1)

Abstract: We characterize having Borel isomorphism relation among some weakly minimal trivial theories, namely the examples of families of finite equivalence relations from recent joint work with Laskowski, and tame expansions of crosscutting-equivalence relations. We also prove a dichotomy in Borel complexity for the latter.