About

I, Kameryn J Williams, am a PhD student in mathematics at the CUNY Graduate Center working under Joel David Hamkins, scheduled to defend my dissertation in Spring 2018. My cv, which contains my contact info, can be found here. See also my publications and my talks.

My research interests lie mainly in set theory. My dissertation is on the structure of models of second-order set theories. Related to my dissertation but not actually in it, I am interested in the foundations of class forcing and in models of arithmetic, both first-order and second-order. More broadly I am interested in forcing and large cardinals and in the connections set theory has to other areas in logic.

kameryn

The title of my blog comes from a couple of properties which can be had by models of set theory or of arithmetic. A model is recursively saturated if it realizes every finitely consistent recursive type. A model is rather classless if its only amenable classes are the definable classes. The construction of models which are both recursively saturated and rather classless is due to Kaufmann. His models are also \omega_1-like, meaning that they are uncountable but any initial segment of them is countable. For some details, see this blog post of mine, chapter 10 of Kossak and Schmerl’s The Structure of Models of Peano Arithmetic, or Kaufmann’s paper “A rather classless model“.

You can find me on mathoverflow, on twitter, and on google+. I also have a separate teaching blog for communicating with my students.

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