Monday, April 23, 2012, 4:00 PM
Speaker: Dima Sinapova
Title: A Bad Scale and the Failure of SCH at $\aleph_\omega$ (part 1)
Starting from a supercompact, we construct a model in which SCH fails at $\aleph_\omega$ and there is a bad scale at $\aleph_\omega$. The existence of a bad scale implies the failure of weak square. The construction uses two Prikry type forcings defined in different ground models and a suitably defined projection between them.
This is joint work with Spencer Unger.