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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<HTML><HEAD><TITLE>ZF/Constructible/README</TITLE></HEAD><BODY>
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<H1>Constructible--Relative Consistency of the Axiom of Choice</H1>
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<P>Gödel's proof of the relative consistency of the axiom of choice is
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mechanized using Isabelle/ZF. The proof builds upon a previous mechanization
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of the
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<A HREF="http://www.cl.cam.ac.uk/users/lcp/papers/Sets/reflection.pdf">reflection
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theorem</A>. The heavy reliance on metatheory in the original proof makes the
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formalization unusually long, and not entirely satisfactory: two parts of the
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proof do not fit together. It seems impossible to solve these problems
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without formalizing the metatheory. However, the present development follows
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a standard textbook, Kunen's <STRONG>Set Theory</STRONG>, and could support the
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formalization of further material from that book. It also serves as an
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example of what to expect when deep mathematics is formalized.
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A paper describing this development is
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<A HREF="http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-551.pdf">available</A>.
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<HR>
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<P>Last modified $Date$
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<ADDRESS>
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<A
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HREF="http://www.cl.cam.ac.uk/users/lcp/">Larry Paulson</A>,
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<A HREF="mailto:lcp@cl.cam.ac.uk">lcp@cl.cam.ac.uk</A>
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</ADDRESS>
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</BODY></HTML>
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