Martin's maximum revisited
Logic
2012-02-10 v2
Abstract
We present several results relating the general theory of the stationary tower forcing developed by Woodin with forcing axioms. The main results is that the forcing axiom MM^{++} (also known as MM^{+\omega_1}) decides the \Pi_2-theory of H_{\omega_2} with respect to stationary set preserving forcings. We argue that this is a close to optimal generalization to H_{\omega_2} of Woodin's absoluteness results for L(R).
Keywords
Cite
@article{arxiv.1110.1181,
title = {Martin's maximum revisited},
author = {Matteo Viale},
journal= {arXiv preprint arXiv:1110.1181},
year = {2012}
}
Comments
31 pages, updated versions will be available on the author's webpage: http://www2.dm.unito.it/paginepersonali/viale/