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From: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Newsgroups: net.math
Subject: Re: Compactness Theorem Help needed
Message-ID: <12114@ucbvax.BERKELEY.EDU>
Date: Sat, 1-Mar-86 16:21:05 EST
Article-I.D.: ucbvax.12114
Posted: Sat Mar  1 16:21:05 1986
Date-Received: Sun, 2-Mar-86 19:15:51 EST
References: <900@kuling.UUCP>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: weemba@brahms.UUCP (Matthew P. Wiener)
Organization: University of California, Berkeley
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In article <900@kuling.UUCP> patrikl@kuling.UUCP (Patrik Lindvall) writes:
>Help needed in producing a proof of the compactness theorem in first order
>predicate Logic, however the completeness theorem may not be used.
>I am in a hurry and Dirk van Dalen's "Logic and Structure" wasn't
> much of a help (or I didn't understand it properly).

You don't want to use the completeness theorem???  They are practically the
same theorem, so it's not easy!  The ultrafilter proof (see for example
Chang and Keisler, _Model Theory_, Section 4.1) gets it directly, but then
you have to learn about ultrafilters (same reference).  C&K's explanation
of the completeness theorem' proof is also very good.

ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720