Martin's maximum revisited
arXiv:1110.1181
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^{+ω_1}) decides the Π_2-theory of H_{ω_2} with respect to stationary set preserving forcings. We argue that this is a close to optimal generalization to H_{ω_2} of Woodin's absoluteness results for L(R).
31 pages, updated versions will be available on the author's webpage: http://www2.dm.unito.it/paginepersonali/viale/