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HOMOTOPY MODEL THEORY

Published online by Cambridge University Press:  05 October 2020

BRICE HALIMI*
Affiliation:
DÉPARTEMENT D’HISTOIRE ET DE PHILOSOPHIE DES SCIENCES & SPHERE UNIVERSITÉ DE PARISPARIS, FRANCEE-mail: [email protected]

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.

Type
Article
Copyright
© Association for Symbolic Logic 2020

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