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A formalization of forcing and the unprovability of the continuum hypothesis (1904.10570v1)
Published 23 Apr 2019 in cs.LO and math.LO
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.