Miyamoto Tadatoshi: A limit stage for proper iterated forcing of length $\omega$

Friday, August 10 at 1:30pm
Fields institute, Room 230

Abstract: Given any notion of forcing $P$ which is proper, we may form a bigger notion of forcing $Q$ with side conditions in such a way that $Q$ is proper and projects down to $P$. Similary, given any iterated forcing $\langle (P_n, Q_n)\mid n<\omega\rangle$ which iterates the proper partial orders $Q_n$, we may form a bigger notion of forcing $Q$ with side conditions in such a way that $Q$ projects down to each $P_n$.