A formalization of forcing and the unprovability of the continuum hypothesis

Jesse Michael Han; Floris van Doorn

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arXiv · 1904.10570

A formalization of forcing and the unprovability of the continuum hypothesis

Jesse Michael Han·Floris van Doorn

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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 $2^{\omega_2 \times \omega}$ and formally verify the failure of the continuum hypothesis in the resulting model.

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Jesse Michael Han, Floris van Doorn. 2019-04-23. A formalization of forcing and the unprovability of the continuum hypothesis. https://arxiv.org/abs/1904.10570

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