A formalization of forcing and the unprovability of the continuum hypothesis
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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Categories
Logic in Computer Science
Logic
03-04, 03E35, 03E40
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