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

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Abonnement à la liste de diffusion

Orateur(s) Denis Osin - Vanderbilt University,
Titre A topological zero-one law and elementary equivalence of finitely generated groups
Horaire16:00 à 17:15
Diffusion https://u-paris.zoom.us/rec/share/a4tx1Lb7BI3wF_dM-1I759pQ4pnOvjfaB_Fhiihs-AWXTKsL5yjeQKFo_FcbPKPq.cjNFf_LDVZFP-Inx
RésumeThe space of finitely generated marked groups, denoted by G, is a locally compact Polish space whose elements are groups with fixed finite generating sets; the topology on G is induced by the local convergence of the corresponding Caley graphs. We will discuss equivalent characterizations of closed subspaces S of G satisfying the following zero-one law: for any sentence sigma in the infinitary logic L_{\omega_1, \omega}, the set of all models of sigma in S is either meager or comeager. In particular, this zero-one law holds for certain natural spaces associated to hyperbolic groups and their generalizations. We will also discuss some open problems.
AdresseSophie Germain