Séminaires : Séminaire de Logique Lyon-Paris

Equipe(s) : lm,
Responsables :S. Anscombe, O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati
Email des responsables :
Salle : Contacter Silvain Rideau ou Alessandro Vignati
Adresse :
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Orateur(s) Laura Fontanella - Université Paris Est,
Titre Realizability and the Axiom of Choice
Date24/03/2021
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.
SalleContacter Silvain Rideau ou Alessandro Vignati
Adresse
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