# Algebra Seminar talk

10:15

Ralf **Schindler***Martin's Maximum is $\Pi_2$-complete*

Abstract:

Every $\Pi_2$ statement about the collection of sets which are
hereditarily at most of size $\aleph_1$ which is consistent in a strong form is
true in the $P_\max$ extension of $L(R)$. This is due to W.H. Woodin and is often
referred to as "$\Pi_2$-maximality."
Inspired by my proof with D. Asperó of "$MM^{++}\Rightarrow (*)$" I will present a direct proof of the result in the title; no
knowledge of $P_\max$ will be presupposed, in fact the proof is "$P_\max$-free."

This is joint work with D. Asperó.