Journal
BULLETIN OF SYMBOLIC LOGIC
Volume 20, Issue 4, Pages 491-496Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/bsl.2014.33
Keywords
stable formula; order property; definable type; relative weak compactness
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Funding
- Institut Universitaire de France
- ANR [ANR-11-JS01-008]
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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 Criteres de compacite 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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