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Sur une application possible du concept d'homotopie à la théorie des modèles

Résumé : This paper endeavors to show the possible application to model theory of concepts coming from modern homotopy theory. In particular, the concept of simplicial set can be brought into play to describe the formulas of a first-order language L, the definable subsets of an L-structure, as well as the type spaces of a theory expressed in L. It is shown that to any L-structure can be associated a simplicial set, according to a functorial mapping that associates simplicial maps to elementary embeddings. Finally, a comparison is sketched between elementary classes of models (in the model-theoretic sense) and model categories (in the homotopy-theoretic sense).
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https://hal-univ-paris10.archives-ouvertes.fr/hal-01551276
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Submitted on : Friday, June 30, 2017 - 10:31:17 AM
Last modification on : Friday, May 29, 2020 - 11:05:39 AM

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Brice Halimi. Sur une application possible du concept d'homotopie à la théorie des modèles. Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2013, 22 (5: Numéro Spécial à l’occasion du Workshop Homotopie, 20-21 octobre 2011, Institut mathématique de Toulouse), pp.1017-1043. ⟨10.5802/afst.1394⟩. ⟨hal-01551276⟩

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