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<h1>Constructible--Relative Consistency of the Axiom of Choice</h1>
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
<a href="http://www.cl.cam.ac.uk/users/lcp/papers/Sets/reflection.pdf">reflection
theorem</a>. 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 <strong>Set Theory</strong>, 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
<a href="http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-551.pdf">available</a>.
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Last modified $Date$
<address>
<a href="http://www.cl.cam.ac.uk/users/lcp/">Larry Paulson</a>,
<a href="mailto:lcp@cl.cam.ac.uk">lcp@cl.cam.ac.uk</a>
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