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FIRST-ORDER HOMOTOPICAL LOGIC

Part of: Categories with structure Applied homological algebra and category theory Categories and theories

Published online by Cambridge University Press:  18 September 2023

JOSEPH HELFER Open the ORCID record for JOSEPH HELFER [Opens in a new window]
JOSEPH HELFER*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF SOUTHERN CALIFORNIA 3620 SOUTH VERMONT AVENUE KAP 104, LOS ANGELES CA 90089-2532, USA
*
E-mail: jhelfer@usc.edu
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Abstract

We introduce a homotopy-theoretic interpretation of intuitionistic first-order logic based on ideas from Homotopy Type Theory. We provide a categorical formulation of this interpretation using the framework of Grothendieck fibrations. We then use this formulation to prove the central property of this interpretation, namely homotopy invariance. To do this, we use the result from [8] that any Grothendieck fibration of the kind being considered can automatically be upgraded to a two-dimensional fibration, after which the invariance property is reduced to an abstract theorem concerning pseudonatural transformations of morphisms into two-dimensional fibrations.

Keywords

homotopy type theoryGrothendieck fibrationsintuitionistic logicmodel categoriescategorical logic2-categories

MSC classification

Primary: 18C50: Categorical semantics of formal languages
Secondary: 18D30: Fibered categories 55U35: Abstract and axiomatic homotopy theory
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 63
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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