Model theoretic stability and definability of types, after A. Grothendieck

Itaï Ben Yaacov (1, 2)

1 ICJ - Institut Camille Jordan
2 AGL - Algèbre, géométrie, logique

We point out how the ''Fundamental Theorem of Stability Theory'', namely the equivalence between the ''non order property'' and definability of types, proved by Shelah in the 1970s, is in fact an immediate consequence of Grothendieck's ''Critères de compacité'' from 1952. The familiar forms for the defining formulae then follow using Mazur's Lemma regarding weak convergence in Banach spaces.

Mots clés: order property; definable type; stable formula; relative weak compactness

Domaines: Logique [math.LO]; Analyse fonctionnelle [math.FA]

Itaï Ben Yaacov. Model theoretic stability and definability of types, after A. Grothendieck. Bulletin of Symbolic Logic, 2014, 20 (4), pp.491-496. ⟨hal-00838148v3⟩