[net.math] Compactness Theorem Help needed

patrikl@kuling.UUCP (Patrik Lindvall) (02/25/86)

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).



-- 
 Patrik Lindvall, Computer Science, University of Uppsala, Sweden

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weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/02/86)

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