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From: hbe@sonia.math.ucla.edu (H. Enderton)
Newsgroups: comp.theory
Subject: Re: Math Logic
Keywords: proof model
Message-ID: <213@kaos.MATH.UCLA.EDU>
Date: 6 Aug 90 23:06:11 GMT
References: <1990Aug3.162306.29574@wiis.wang.com>
Sender: news@MATH.UCLA.EDU
Reply-To: hbe@math.ucla.edu (H. Enderton)
Distribution: sci.logic
Organization: UCLA Mathematics Department
Lines: 12

In article <1990Aug3.162306.29574@wiis.wang.com> bnh@wiis.wang.com
(Bill Halchin) asks about the connection between provability (with
axioms and rules of inference) and logical consequence (defined
semantically).

The remarkable connection between provability and logical consequence
(for first-order logic) is given by the Godel completeness theorem.
(Not to be confused with the Godel incompleteness theorem.)  Since you
have Kleene's book, see section 72.  The completeness theorem must be
in Boolos & Jeffrey also (which is probably a better place to start).

--hbe