From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!utgpu!cs.utexas.edu!uunet!trwacs!erwin Tue May 12 15:49:40 EDT 1992
Article 5480 of comp.ai.philosophy:
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>From: erwin@trwacs.fp.trw.com (Harry Erwin)
Newsgroups: comp.ai.philosophy
Subject: Re: Goedel's theorem proof without self-referencing?
Message-ID: <573@trwacs.fp.trw.com>
Date: 8 May 92 12:29:23 GMT
References: <1992Apr23.183732.25378@kum.kaist.ac.kr> <1992May4.214051.16767@hellgate.utah.edu> <76781@netnews.upenn.edu> <2358@ariel.its.unimelb.EDU.AU> <77079@netnews.upenn.edu>
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weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:

>In article <2358@ariel.its.unimelb.EDU.AU>, jcollier@ariel (John Donald Collier) writes:
...
>If you identify a property that countable sets must have and that the
>the unit interval [0,1] does not, you have shown that the reals are
>uncountable.  I wouldn't call this self-reference.

>The most well-known such property is zero measure (as a subset of [0,1]).

>Gentzen's proof for the incompleteness of PA uses a more subtle property
>to distinguish Con(PA) from PA-provable results.

There are uncountable subsets of [0,1] with zero measure. For example,
some types of Cantor sets and other sets with fractal dimension. 

Cheers,
-- 
Harry Erwin
Internet: erwin@trwacs.fp.trw.com



