| Orateur(s) | Laura Fontanella - Université Paris Est,
|
| Titre | Realizability and the Axiom of Choice |
| Date | 24/03/2021 |
| Horaire | 16:00 à 17:15 |
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| Diffusion | https://u-paris.zoom.us/rec/share/5tQpPLWZAlOTSlrZgCKB90ftESHsHwYceiBLWDbY7DyBbhlLngEJVZN1lTKdedjQ.hwYmhRYAfONlNyoK |
| Résume | Realizability 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. |
| Salle | 1013 |
| Adresse | Sophie Germain |
