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Preprint Number 597
597. Itaï Ben Yaacov
Model theoretic stability and definability of types, after A. Grothendieck
Submission date: 25 June 2013.
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.
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