English

Turing Invariant Sets and the Perfect Set Property

Logic 2020-04-06 v3

Abstract

We show that ZF+DC+ZF+DC+"all Turing invariant sets of reals have the perfect set property" implies that all sets of reals have the perfect set property. We also show that this result generalizes to all countable analytic equivalence relations.

Cite

@article{arxiv.1912.12558,
  title  = {Turing Invariant Sets and the Perfect Set Property},
  author = {Clovis Hamel and Haim Horowitz and Saharon Shelah},
  journal= {arXiv preprint arXiv:1912.12558},
  year   = {2020}
}

Comments

Final version

R2 v1 2026-06-23T12:58:13.053Z