## Logic Seminar

Sittinon Jirattikansakul

CMU

Blowing up the power of singular cardinal of any uncountable cofinality with collapses

**Abstract:**Prikry-type forcings have been developed to tackle problems on singular cardinals. A specific example is the Singular Cardinal Hypothesis (SCH): the size of a powerset of a singular cardinal is the smallest value consistent with ZFC. In particular, if $\theta$ is a singular strong limit cardinal, then $2^\theta=\theta^+$. In 2019, Gitik developed a forcing that violates the SCH, given that the target cardinals were singular in a ground model. In this talk, we will discuss the Gitik's forcing with interleave collapses, to violate the SCH at the small alephs.

Tuesday March 30, 2021 at 4:00 PM in Zoom