On a Fragment of the Universal Baire Property for Sigma^1_2 Sets
Logic
2007-05-23 v3
Abstract
There is a well-known global equivalence between \Sigma^1_2 sets having the Universal Baire property, two-step \Sigma^1_3 generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of \Sigma^1_2 sets being (2^{\omega})^{+}-cc Universally Baire, which is below 0^{#}. In a model obtained, there is a \Sigma^1_2 set which is weakly \omega_2-Universally Baire but not \omega_2-Universally Baire.
Keywords
Cite
@article{arxiv.math/0603540,
title = {On a Fragment of the Universal Baire Property for Sigma^1_2 Sets},
author = {Stuart Zoble},
journal= {arXiv preprint arXiv:math/0603540},
year = {2007}
}