A Proofless Proof of the Barwise Compactness Theorem

Howard, Mark

Howard, Mark

J. Symbolic Logic, Tome 53 (1988) no. 1, p. 597-602 / Harvested from Project Euclid

Résumé

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.

Publié le : 1988-06-14
Classification:

@article{1183742644,
     author = {Howard, Mark},
     title = {A Proofless Proof of the Barwise Compactness Theorem},
     journal = {J. Symbolic Logic},
     volume = {53},
     number = {1},
     year = {1988},
     pages = { 597-602},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183742644}
}

Howard, Mark. A Proofless Proof of the Barwise Compactness Theorem. J. Symbolic Logic, Tome 53 (1988) no. 1, pp.  597-602. http://gdmltest.u-ga.fr/item/1183742644/