## Kameryn J Williams

This is my old website, which I’m keeping around so old links still work and my old blog posts are still available. The information on this site is out of date. You are probably looking for my current website.

I am a mathematician and logician specializing in set theory. I did my PhD at the CUNY Graduate Center under Joel David Hamkins.

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“.