Logic Workshop

September 4
Roman Kossak, CUNY
Lattices of elementary substructures of recursively saturated models of PA

In the 1980s, Henryk Kotlarski published a number of results about elementary cuts in countable recursively saturated models of arithmetic. I will outline some of Kotlarski's main results that motivated him to ask whether the lattice of elementary substructures of a countable recursively saturated model of PA depends on the model. I will outline the proof of a partial answer that Jim Schmerl and I gave a long time ago and I will follow with some new results related to modified versions of Kotlarski's question.