Journal of Symbolic Logic

A Proofless Proof of the Barwise Compactness Theorem

Mark Howard

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We prove a theorem (1.7) about partial orders which can be viewed as a version of the Barwise compactness theorem which does not mention logic. The Barwise compactness theorem is easily equivalent to 1.7 + "Every Henkin set has a model". We then make the observation that 1.7 gives us the definability of forcing for quantifier-free sentences in the forcing language and use this to give a direct proof of the truth and definability lemmas of forcing.

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J. Symbolic Logic, Volume 53, Issue 2 (1988), 597-602.

First available in Project Euclid: 6 July 2007

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Howard, Mark. A Proofless Proof of the Barwise Compactness Theorem. J. Symbolic Logic 53 (1988), no. 2, 597--602.

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