Proofs and algorithms seminar: Yorgo Chamoun on Wednesday 06 November 2024 at 14h30
===== Seminar of the proofs and algorithms pole =====
Hello everybody,
For a new seminar of the proofs and algorithms pole of LIX, we are happy to welcome Yorgo Chamoun (Cosynus), invited by the Cosynus team.
***** Wednesday 06 November 2024 at 14h30, room Philippe Flajolet *****
Yorgo Chamoun -- De Morgan toposes and model theory
De Morgan's law, also known as "weak excluded middle", is expressed in a Heyting algebra (hence in intuitionistic logic) by the equality ¬x ∨ ¬¬x = 1 for any element x of the algebra. On the other hand, a topos is a "pastiche" category of the category of sets, and therefore admits an internal language that is at least intuitionistic. We can therefore naturally define a De Morgan topos as a topos whose internal logic admits De Morgan's law, but an "external" approach, without any mention of the internal logic, is possible and is very practical to handle. The aim of this presentation will be to illustrate different facets of these toposes, adopting this external approach. Firstly, we will attempt to establish links with model theory and, more specifically, the amalgamation property, via the notion of classifying topos of a geometric theory. Secondly, we will show how a De Morgan topos can be associated in a more or less canonical way with any topos, and the contributions in this field of the tools recently introduced by Caramello for studying (among other things) the internal locales of a topos.
The following seminar will be on Tuesday 12 November 2024 at 14h00 by Louis Lemonnier: A recipe for the semantics of reversible programming.
The list of upcoming seminars can be found at:
https://www.lix.polytechnique.fr/proofs-algorithms/seminar/
The calendar of seminars can be found at:
https://www.lix.polytechnique.fr/proofs-algorithms/seminar/calendar.ics