Complexity of Ramsey null sets
Logic
2010-04-01 v1
Abstract
We show that the set of codes for Ramsey positive analytic sets is -complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the set of codes for uncountable analytic sets is -complete. This shows a close resemblance between the Sacks forcing and the Mathias forcing. In particular, we get that the -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}
}