J. D. Hamkins, A new large-cardinal never-indestructibility phenomenon, PSC-CUNY Enhanced Research Award 45, funded for 2014-2015.
Abstract. Professor Hamkins proposes to undertake research in the area of logic and foundations known as set theory, focused on the interaction of forcing and large cardinals. In a first project, he will investigate a new large cardinal non-indestructibility phenomenon, recently discovered in his joint work with Bagaria, Tsaprounis and Usuba. In a second project, continuing joint work with Cody, Gitik and Schanker, he will investigate new instances of the identity-crises phenomenon between weak compactness and other much stronger large cardinal notions.