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Model theoretic stability and definability of types, after A. Grothendieck
- Source :
- Bulletin of Symbolic Logic, Association for Symbolic Logic, 2014, 20 (4), pp.491-496
- Publication Year :
- 2013
-
Abstract
- 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 "Crit{\`e}res de compacit{\'e}" from 1952. The familiar forms for the defining formulae then follow using Mazur's Lemma regarding weak convergence in Banach spaces.
- Subjects :
- Mathematics - Logic
Mathematics - Functional Analysis
Subjects
Details
- Database :
- arXiv
- Journal :
- Bulletin of Symbolic Logic, Association for Symbolic Logic, 2014, 20 (4), pp.491-496
- Publication Type :
- Report
- Accession number :
- edsarx.1306.5852
- Document Type :
- Working Paper