Martin's maximum revisited
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+ω1) decides the 2-theory of Hω2 with respect to stationary set preserving forcings. We argue that this is a close to optimal generalization to Hω2 of Woodin's absoluteness results for L(R).
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