### 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.