First steps towards a formalization of Forcing

07/13/2018

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by   Emmanuel Gunther, et al.

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We lay the ground for an Isabelle/ZF formalization of Cohen's technique of forcing. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize a version of the principle of Dependent Choices and using it we prove the Rasiowa-Sikorski lemma on the existence of generic filters. Given a transitive set M, we define its generic extension M[G], the canonical names for elements of M, and finally show that if M satisfies the axiom of pairing, then M[G] also does.