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SAS

Seminar

The relative consistency of the axiom of choice mechanized using Isabelle/ZF

Paulson, L (University of Cambridge)
Thursday 22 March 2012, 13:30-15:00

Discussion Room, Newton Institute

Abstract

The 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. However, 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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