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

Author Robert Passmann

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Author Details

Robert Passmann
  • Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands

Funding

This research was partially supported by the Studienstiftung des deutschen Volkes (German Academic Scholarship Foundation).

Acknowledgements

I would like to thank Lorenzo Galeotti, Joel Hamkins, Rosalie Iemhoff, Dick de Jongh, Yurii Khomskii, and Benedikt Löwe for helpful and inspiring discussions.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.CSL.2020.33

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constructive mathematics
  • Theory of computation → Proof theory
Keywords
  • Intuitionistic Logic
  • Intuitionistic Set Theory
  • Constructive Set Theory

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