## Logic Seminar

Justin MooreCornell University
Woodin's $\mathbb{P}_{\mathrm{max}}$-extension
Wednesday, September 18, 2019 - 4:00pm
Malott 206

In the presence of a supercompact cardinal, the theory of Solovay's model $L(\mathbf{R})$ cannot be changed by forcing. Given that $L(\mathbf{R})$ fails to satisfy the Axiom of Choice, it is natural to wonder if this inner model can be enlarged in a controlled way to obtain a model of ZFC. Woodin's $\mathbb{P}_{\mathrm{max}}$-extension of $L(\mathbf{R})$ is such an enlargement. It has a theory which, in many ways, mirrors the theory of Martin's Maximum, the forcing axiom for stationary set preserving forcings. This talk will give an introduction to the $\mathbb{P}_{\mathrm{max}}$-extension and its properties. This topic will be further developed in the Wednesday lectures in this semester (fall 2019).