# Indestructibility for Ramsey cardinals

## Victoria Gitman

### The City University of New York

A large cardinal $\kappa$ is said to be indestructible by a certain poset $\mathbb P$ if $\kappa$ retains the large cardinal property in all forcing extensions by $\mathbb P$. Since most relative consistency results for ${\rm ZFC}$ are obtained via forcing, the knowledge of a large cardinal’s indestructibility properties is used to establish the consistency of that large cardinal with other set theoretic properties. In this talk, I will use an elementary embeddings characterization of Ramsey cardinals to prove some basic indestructibility results.

Victoria Gitman received her Ph.D. in 2007 from the CUNY Graduate Center, as a student of Joel Hamkins, and is presently a visiting scholar at the CUNY Graduate Center. Her research is in Mathematical Logic, in particular in the areas of Set Theory and Models of Peano Arithmetic.