Martin's maximum revisited

We present several results relating the general theory of the stationary tower forcing developed by Woodin with forcing axioms. In particular we show that, in combination with strong large cardinals, the forcing axiom MM++ makes the Π2-fragment of the theory of Hℵ2 invariant with respect to stationary set preserving forcings that preserve BMM. We argue that this is a close to optimal generalization to Hℵ2 of Woodin’s absoluteness results for L( ). In due course of proving this we shall give a new proof of some of Woodin’s results.

• Type: Journal
• Year: 2016
• Where: AML
• Authors: Matteo Viale
• Keywords: Algorithms, AML 2016