# Séminaires : Séminaire Général de Logique

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

 Orateur(s) Matteo Viale - Université de Turin, Titre Tameness for Set Theory Date 02/03/2020 Horaire 15:15 à 16:15 Diffusion Résume We show that (assuming large cardinals) set theory is a tractable (and we dare to say tame)  first order theory when formalized in a first order signature with natural predicate symbols for the basic  definable concepts of second and third order arithmetic, and appealing to the model-theoretic notions of model completeness and model companionship.  Specifically we develop a general framework linking  generic absoluteness results to model companionship and show that (with the required care in details)  a $\Pi_2$-property formalized in an appropriate language for second or third order number theory  is forcible from some  $T\supseteq\ZFC+$\emph{large cardinals} if and only if it is consistent with the universal fragment of $T$ if and only if it is realized in the model companion of $T$. Salle 2015 Adresse Sophie Germain