Amoeba-absoluteness and projective measurability
Logic
2009-09-25 v1
Abstract
We study the relationship between Amoeba forcing (the partial order which generically adds a measure one set of random reals) and projective measurability. Given a universe V of set theory and a forcing notion P in V we say that V is Sigma^1_n - P - absolute iff for every Sigma^1_n-sentence phi with parameters in V we have V models phi iff V^P models phi. We show that Sigma^1_4-Amoeba-absoluteness implies that forall a in omega^omega (omega_1^{L[a]} < omega_1^V), and hence Sigma^1_3-measurability. This answers a question of Haim Judah (private communication).
Cite
@article{arxiv.math/9209206,
title = {Amoeba-absoluteness and projective measurability},
author = {Jörg Brendle},
journal= {arXiv preprint arXiv:math/9209206},
year = {2009}
}