Computability in Europe 2008
Logic and Theory of Algorithms

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Special Session Talk:
The relative consistency of the axiom of choice mechanized using Isabelle/ZF

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Speaker: Lawrence C Paulson


Gödel's proof of the relative consistency of the axiom of choice has been mechanized using Isabelle/ZF, building on a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the formalization unusually long, and not entirely satisfactory: two parts of the proof do not fit together. It seems impossible to solve these problems without formalizing the metatheory, which would make the proof quite different from Gödel's. The present development follows a standard textbook, Kenneth Kunen's Set theory: an introduction to independence proofs, and could support the formalization of further material from that book. It also serves as an example of what to expect when deep mathematics is formalized.

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