19 February 2020, Algebra|Coalgebra Seminar, Iris van der Giessen

Abstract:
I would like to present ongoing work on intuitionistic modal logics iGL and iSL which have a close connection to the (unknown!) provability logic of Heyting Arithmetic. Classically, Gödel-Löb logic GL admits a provability interpretation for Peano Arithmetic. iGL is its intuitionistic counterpart and iSL is iGL extended by explicit completeness principles. I will characterize both systems via an axiomatization and in terms of Kripke models. The main goal is to understand their admissible rules in order to get insight in the structure of those logics. To do so, I want to focus on one step in this direction: Ghilardi’s wonderful result connecting projective formulas to the extension property in Kripke models.