I, Kameryn J Williams, am a mathematician and logician. I am a postdoc in the mathematics department at University of Hawai‘i at Mānoa. My PhD is from The Graduate Center of The City University of New York.
Speaking at the Kurt Gödel Research Center about the strength of the class forcing theorem.
My main research interests are in set theory. Much of my work is motivated by the multiversist perspective in set theory, as advanced by Joel David Hamkins—whom I was lucky to have as an advisor at CUNY—and others. Multiversism is the position that there is a plurality of conceptions of set, each giving rise to a different set theoretic universe, rather than a single, ultimate universe of sets. This perspective raises many interesting mathematical questions. Presented very generally: What universes of sets are possible and what properties can they have? What is the structure of the multiverse as a whole? My dissertation is specifically focused on the case of second-order set theory, i.e. set theory with proper classes as actual objects, rather than mere syntactic sugar. Most recently, my coauthors and I recently put out a preprint of a paper on (non)amalgamability in the generic multiverse.
Besides my interest in pure set theory I am interested in its connections to other areas of logic. Some of my set theoretic work naturally ties into the model theory of models of set theory, and I make good use of admissible set theory, which sits at the intersection of set theory, computability theory, and model theory. I also maintain an interest in models of arithmetic. See the research tab on the navigation bar for more information.
Besides my research work, I am fortunate to have a job where I can share my love of mathematics with my students. There is a depth and beauty to mathematics which I believe everyone can learn and appreciate. Students, see the teaching tab on the navigation bar for information about classes, syllabi, homework, etc.
I also keep a web log where I post snippets of mathematical interest. See the corresponding tab in the navigation bar, where you can also find an online version of my CV and contact information.