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.ITP.2019.19
URN: urn:nbn:de:0030-drops-110742
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11074/
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Han, Jesse Michael ; van Doorn, Floris

A Formalization of Forcing and the Unprovability of the Continuum Hypothesis

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LIPIcs-ITP-2019-19.pdf (0.6 MB)

Abstract

We describe a formalization of forcing using Boolean-valued models in the Lean 3 theorem prover, including the fundamental theorem of forcing and a deep embedding of first-order logic with a Boolean-valued soundness theorem. As an application of our framework, we specialize our construction to the Boolean algebra of regular opens of the Cantor space 2^{omega_2 x omega} and formally verify the failure of the continuum hypothesis in the resulting model.

BibTeX - Entry

@InProceedings{han_et_al:LIPIcs:2019:11074,
  author =	{Jesse Michael Han and Floris van Doorn},
  title =	{{A Formalization of Forcing and the Unprovability of the Continuum Hypothesis}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{John Harrison and John O'Leary and Andrew Tolmach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11074},
  URN =		{urn:nbn:de:0030-drops-110742},
  doi =		{10.4230/LIPIcs.ITP.2019.19},
  annote =	{Keywords: Interactive theorem proving, formal verification, set theory, forcing, independence proofs, continuum hypothesis, Boolean-valued models, Lean}
}

Keywords: Interactive theorem proving, formal verification, set theory, forcing, independence proofs, continuum hypothesis, Boolean-valued models, Lean
Collection: 10th International Conference on Interactive Theorem Proving (ITP 2019)
Issue Date: 2019
Date of publication: 05.09.2019
Supplementary Material: https://github.com/flypitch/flypitch

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