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DOI: 10.4230/LIPIcs.CSL.2020.33

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

Authors: Robert Passmann

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

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.

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Robert Passmann. De Jongh’s Theorem for Intuitionistic Zermelo-Fraenkel Set Theory. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{passmann:LIPIcs.CSL.2020.33,
  author =	{Passmann, Robert},
  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 =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.33},
  URN =		{urn:nbn:de:0030-drops-116767},
  doi =		{10.4230/LIPIcs.CSL.2020.33},
  annote =	{Keywords: Intuitionistic Logic, Intuitionistic Set Theory, Constructive Set Theory}
}

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

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