# Dima Sinapova: A bad scale and the failure of SCH at $\aleph_\omega$ (part 2)

Monday, May 7, 2012, 4:00 PM
RH 440R

Speaker: Dima Sinapova (UCI)

Title: A bad scale and the failure of SCH at $\aleph_\omega$ II

Abstract:

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.