License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2020.33
URN: urn:nbn:de:0030-drops-116767
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11676/
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Passmann, Robert

De Jongh’s Theorem for Intuitionistic Zermelo-Fraenkel Set Theory

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LIPIcs-CSL-2020-33.pdf (0.5 MB)

Abstract

We prove that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional logic IPC. More generally, we show that IZF has the de Jongh property with respect to every intermediate logic that is complete with respect to a class of finite trees. The same results follow for constructive set theory CZF.

BibTeX - Entry

@InProceedings{passmann:LIPIcs:2020:11676,
  author =	{Robert Passmann},
  title =	{{De Jongh’s Theorem for Intuitionistic Zermelo-Fraenkel Set Theory}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11676},
  URN =		{urn:nbn:de:0030-drops-116767},
  doi =		{10.4230/LIPIcs.CSL.2020.33},
  annote =	{Keywords: Intuitionistic Logic, Intuitionistic Set Theory, Constructive Set Theory}
}

Keywords: Intuitionistic Logic, Intuitionistic Set Theory, Constructive Set Theory
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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