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“.