KGRC Research seminar on 2017-10-19 at 4pm.
Speaker: Monroe Eskew (KGRC)
Abstract: Instances of Chang’s Conjecture (CC) can be seen as a generalization of the Loweheim-Skolem Theorem to a logic in between those the first and second order. Foreman asked how far the analogy with Lowenheim-Skolem can go, specifically whether a global version of CC is consistent. In joint work with Yair Hayut, the speaker answered Foreman’s question affirmatively, and in the process lowered the known upper bounds on consistency strength for many instances of CC. We will discuss the results, as well as some barriers that singular cardinal combinatorics impose on the possibility of a stronger global CC.