I, Kameryn J Williams, am a PhD student in mathematics at the CUNY Graduate Center working under Joel David Hamkins. My research interests lie mainly in set theory. My dissertation is on the structure of models of second-order set theories, primarily Gödel-Bernays set theory and Kelley-Morse set theory. Outside of my dissertation topic, I am interested in forcing and large cardinals and in models of arithmetic, both first-order and second-order.
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 -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“.