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HOMOTOPY MODEL THEORY

Part of: Applied homological algebra and category theory Model theory

Published online by Cambridge University Press:  05 October 2020

BRICE HALIMI
BRICE HALIMI*
Affiliation:
DÉPARTEMENT D’HISTOIRE ET DE PHILOSOPHIE DES SCIENCES & SPHERE UNIVERSITÉ DE PARISPARIS, FRANCEE-mail: brice.halimi@u-paris.fr
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Abstract

Drawing on the analogy between any unary first-order quantifier and a “face operator,” this paper establishes several connections between model theory and homotopy theory. The concept of simplicial set is brought into play to describe the formulae of any first-order language L, the definable subsets of any L-structure, as well as the type spaces of any theory expressed in L. An adjunction result is then proved between the category of o-minimal structures and a subcategory of the category of linearly ordered simplicial sets with distinguished vertices.

Keywords

quantifiers as face operatorsdefinable subsetstype spaceso-minimalitysimplicial setsfibrationshomotopical algebra

MSC classification

Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 03C95: Abstract model theory 55U10: Simplicial sets and complexes
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 4 , December 2021 , pp. 1301 - 1323
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Copyright
© Association for Symbolic Logic 2020

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