## Kameryn J Williams

Welcome to my website!

I am a mathematician and logician specializing in set theory. My PhD work was done at The Graduate Center, CUNY, and I’ll be graduating in May 2018. Joel David Hamkins was my adviser, and my dissertation was about models of second-order set theories. Outside of my dissertation work, I am interested in class forcing, both its foundations and applications; the model theory of arithmetic; forcing and large cardinals; and the philosophy of set theory.

My blog posts can be found here.

Various pages that may be of interest to you:

Me talking to the Kurt Gödel Research Center about the strength of the class forcing theorem.

The title of my site 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“.