On the Role of the Baire Category Theorem and Dependent Choice in the Foundations of Logic

Goldblatt, Robert

J. Symbolic Logic, Tome 50 (1985) no. 1, p. 412-422 / Harvested from Project Euclid

Résumé

The Principle of Dependent Choice is shown to be equivalent to: the Baire Category Theorem for Cech-complete spaces (or for complete metric spaces); the existence theorem for generic sets of forcing conditions; and a proof-theoretic principle that abstracts the "Henkin method" of proving deductive completeness of logical systems. The Rasiowa-Sikorski Lemma is shown to be equivalent to the conjunction of the Ultrafilter Theorem and the Baire Category Theorem for compact Hausdorff spaces.

Publié le : 1985-06-14
Classification:

@article{1183741848,
     author = {Goldblatt, Robert},
     title = {On the Role of the Baire Category Theorem and Dependent Choice in the Foundations of Logic},
     journal = {J. Symbolic Logic},
     volume = {50},
     number = {1},
     year = {1985},
     pages = { 412-422},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183741848}
}

Goldblatt, Robert. On the Role of the Baire Category Theorem and Dependent Choice in the Foundations of Logic. J. Symbolic Logic, Tome 50 (1985) no. 1, pp.  412-422. http://gdmltest.u-ga.fr/item/1183741848/