December 6
Roman Kossak,
CUNY
Lattices of elementary submodels of recursively saturated models of PA
Much work on elementary submodels of recursively saturated models of PA was done, beginning in the 1980s, by Craig Smoryński, Richard Kaye, Henryk Kotlarski, Jim Schmerl, and myself. The set of all elementary substructures of a recursively saturated model $M$ ordered by inclusion forms a lattice $Lt(M)$. Kotlarski asked whether $Lt(M)$ depends on $M$. In the talk, I will describe the architecture of $Lt(M)$, and I will survey what is known and what is still open about Kotlarski's question.