English

Hyper-hyperfiniteness and complexity

Logic 2024-09-26 v1

Abstract

We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite then the complexity of hyperfinite countable Borel equivalence relations is as high as possible, namely, Σ21\Sigma^1_2-complete.

Keywords

Cite

@article{arxiv.2409.16445,
  title  = {Hyper-hyperfiniteness and complexity},
  author = {Joshua Frisch and Forte Shinko and Zoltan Vidnyanszky},
  journal= {arXiv preprint arXiv:2409.16445},
  year   = {2024}
}