License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.87
URN: urn:nbn:de:0030-drops-145272
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14527/
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Trotta, Davide ; Spadetto, Matteo ; de Paiva, Valeria

The Gödel Fibration

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LIPIcs-MFCS-2021-87.pdf (0.8 MB)

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.

BibTeX - Entry

@InProceedings{trotta_et_al:LIPIcs.MFCS.2021.87,
  author =	{Trotta, Davide and Spadetto, Matteo and de Paiva, Valeria},
  title =	{{The G\"{o}del Fibration}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{87:1--87:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14527},
  URN =		{urn:nbn:de:0030-drops-145272},
  doi =		{10.4230/LIPIcs.MFCS.2021.87},
  annote =	{Keywords: Dialectica category, G\"{o}del fibration, Pseudo-monad}
}

Keywords: Dialectica category, Gödel fibration, Pseudo-monad
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021

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