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arXiv:1110.1181 [math.LO]AbstractReferencesReviewsResources

Martin's maximum revisited

Matteo Viale

Published 2011-10-06, updated 2012-02-09Version 2

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).

Comments: 31 pages, updated versions will be available on the author's webpage: http://www2.dm.unito.it/paginepersonali/viale/
Categories: math.LO
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