A formalization of forcing and the unprovability of the continuum hypothesis

04/23/2019

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by   Jesse Michael Han, et al.

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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^ω_2 ×ω and formally verify the failure of the continuum hypothesis in the resulting model.