Séminaires : Séminaire de Logique Lyon-Paris

Equipe(s) : lm,
Responsables :S. Anscombe, O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati
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Orateur(s) Matteo Viale - Université de Turin,
Titre Tameness for Set Theory
Horaire15:15 à 16:15

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 $T$.

AdresseSophie Germain