J. D. Hamkins, Research in set theory, PSC-CUNY Enhanced Research Award 42, 2011-2012.

Abstract.  The Principal Investigator, Professor Hamkins, pursues an active research program, with a stream of scholarly publications, international invitations to speak and distinguished grants, and is active in graduate education, currently supervising four PhD students. Professor Hamkins proposes to undertake research in the area of mathematical logic known as set theory, pursuing several projects unified by the classical Boolean ultrapower construction. Specifically, he seeks to investigate the extent to which various large cardinal extender embeddings are realized as Boolean ultrapowers, with their accompanying canonical generic objects, and to investigate the generalized Bukovsky-Dehornoy phenomenon, among other applications of the Boolean ultrapower. Professor Hamkins has a solid publication record on the topics broadly surrounding the proposed research, and has been a leading researcher on the

particular topic proposed.