Constructible--Relative Consistency of the Axiom of Choice
Gödel's proof of the relative consistency of the axiom of choice is
mechanized using Isabelle/ZF. The proof builds upon 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, Kunen's Set Theory, 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.
A paper describing this development is
available.
Last modified $Date: 2005/03/07 18:19:12 $
Larry Paulson,
lcp@cl.cam.ac.uk