Journal of Symbolic Logic

A Proofless Proof of the Barwise Compactness Theorem

Mark Howard

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742644

Mathematical Reviews number (MathSciNet)
MR947861

Zentralblatt MATH identifier
0652.06005

JSTOR
links.jstor.org

Citation

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


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