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DOI: 10.4230/LIPIcs.ITP.2019.19
URN: urn:nbn:de:0030-drops-110742
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11074/
Han, Jesse Michael ; van Doorn, Floris
A Formalization of Forcing and the Unprovability of the Continuum Hypothesis
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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 | |
| Seminar: | 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 |
