# Seminar

Thursday, 26 October 2023, Sala Verde (Ca’ Vignal 3 - La Piramide).

10:30

Samuele Maschio (Università degli Studi di Padova)

*Implicative models of set theory*

Implicative algebras were introduced by A.Miquel to provide a common foundation for Heyting/Boolean-valued logic and realizability. In this talk I will show how one can produce models for intuitionistic and classical Zermelo-Fraenkel set theory (I)ZF using implicative algebras, generalizing forcing and realizability models for set theory, both intuitionistic and classical . This result has an application to the theory of toposes, since it entails that every topos which is obtained from Set by means of the tripos-to-topos construction contains a model of (I)ZF, provided one assumes a large enough inaccessible cardinal exists. This talk is based on a joint work with A.Miquel.