Ralf Schindler: Bounded forcing axioms and reflection

Week 1, Friday June 19, 14:10-15:00

We study mouse reflection in the presence of BPFA, the bounded proper forcing axiom. It turns out that under Woodin's P_max axiom (*), BPFA is equivalent to BMM^{++}, a strong version of bounded Martin's maximum. We also present new information about (dagger), the statement according to which every stationary set preserving forcing is semiproper.