Séminaires : Séminaire Général de Logique

Equipe(s) : lm,
Responsables :S. Anscombe, A. Vignati
Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr
Salle : 1013
Adresse :Sophie Germain


Abonnement à la liste de diffusion

Orateur(s) Laura Fontanella - Université Paris Est,
Titre Realizability and the Axiom of Choice
Horaire16:00 à 17:15
Diffusion https://u-paris.zoom.us/rec/share/5tQpPLWZAlOTSlrZgCKB90ftESHsHwYceiBLWDbY7DyBbhlLngEJVZN1lTKdedjQ.hwYmhRYAfONlNyoK
RésumeRealizability aims at extracting the computational content of mathematical proofs. Introduced in 1945 by Kleene as part of a broader program in constructive mathematics, realizability has later evolved to include classical logic and even set theory. Krivine's work led to define realizability models for the theory ZF following a general technique that generalizes the method of Forcing. However realizing the full Axiom of Choice is quite problematic. After a brief presentation of Krivine's techniques, we will discuss the major obstacles for realizing the Axiom of Choice and I will present my recent joint work with Guillaume Geoffroy that led to realize weak versions of the Axiom of Choice for arbitrarily large cardinals.
AdresseSophie Germain