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The Gödel Fibration

Authors Davide Trotta , Matteo Spadetto, Valeria de Paiva

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Author Details

Davide Trotta
  • Department of Computer Science, University of Pisa, IT
Matteo Spadetto
  • School of Mathematics, University of Leeds, UK
Valeria de Paiva
  • Topos Institute, Berkeley, CA, USA

Funding

  • Trotta, Davide: the research is supported by the MIUR PRIN 2017FTXR "IT-MaTTerS".
  • Spadetto, Matteo: the research is supported by a School of Mathematics Full-Time EPSRC Doctoral Training Partnership Studentship.
  • de Paiva, Valeria: the author acknowledges support from AFOSR grant FA9550-20-10348.

Cite AsGet BibTex

Davide Trotta, Matteo Spadetto, and Valeria de Paiva. The Gödel Fibration. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 87:1-87:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.MFCS.2021.87

Abstract

We introduce the notion of a Gödel fibration, which is a fibration categorically embodying both the logical principles of traditional Skolemization (we can exchange the order of quantifiers paying the price of a functional) and the existence of a prenex normal form presentation for every logical formula. Building up from Hofstra’s earlier fibrational characterization of de Paiva’s categorical Dialectica construction, we show that a fibration is an instance of the Dialectica construction if and only if it is a Gödel fibration. This result establishes an intrinsic presentation of the Dialectica fibration, contributing to the understanding of the Dialectica construction itself and of its properties from a logical perspective.

Subject Classification

ACM Subject Classification
  • Theory of computation → Higher order logic
  • Theory of computation → Proof theory
  • Theory of computation → Constructive mathematics
Keywords
  • Dialectica category
  • Gödel fibration
  • Pseudo-monad

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