# Indestructibility for Ramsey cardinals

Set theory seminarFriday, May 3, 201310:00 amGC 5383

# Indestructibility for Ramsey cardinals

### 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.

Posted by on April 16th, 2013
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## About Joel David Hamkins

Professor Hamkins undertakes research in mathematical logic, especially set theory.