Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 53, Issue 2 (1988), 597-602.
A Proofless Proof of the Barwise Compactness Theorem
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.
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. https://projecteuclid.org/euclid.jsl/1183742644