English

Complexity of Ramsey null sets

Logic 2010-04-01 v1

Abstract

We show that the set of codes for Ramsey positive analytic sets is Σ21\mathbf{\Sigma}^1_2-complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the set of codes for uncountable analytic sets is Σ11\mathbf{\Sigma}^1_1-complete. This shows a close resemblance between the Sacks forcing and the Mathias forcing. In particular, we get that the σ\sigma-ideal of Ramsey null sets is not ZFC-correct. This solves a problem posed by Ikegami, Pawlikowski and Zapletal.

Keywords

Cite

@article{arxiv.1003.5983,
  title  = {Complexity of Ramsey null sets},
  author = {Marcin Sabok},
  journal= {arXiv preprint arXiv:1003.5983},
  year   = {2010}
}
R2 v1 2026-06-21T15:04:51.655Z