Christian Espíndola: Completeness of infinitary intuitionistic logics

In this talk, I will present the second half of my thesis, which relies on classical assumptions and is meant to be a counterpart for the constructive content of the first half. We will define formal systems for infinitary intuitionistic logics and prove completeness theorems in terms of a natural infinitary Kripke semantics, both in the propositional case and the first-order case. The metatheory will be ZFC plus the existence of weakly compact cardinals, a large cardinal assumption that will also be proved to be necessary for the completeness results to hold. We will also review some applications and consequences of these results.