On the role of the baire category theorem and dependent choice in the foundations of logic

Journal of Symbolic Logic 50 (2):412-422 (1985)
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Abstract

The Principle of Dependent Choice is shown to be equivalent to: the Baire Category Theorem for Čech-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

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Citations of this work

Omitting Types for Algebraizable Extensions of First Order Logic.Tarek Sayed Ahmed - 2005 - Journal of Applied Non-Classical Logics 15 (4):465-489.
Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (3):465-516.
The Hahn-Banach Property and the Axiom of Choice.Juliette Dodu & Marianne Morillon - 1999 - Mathematical Logic Quarterly 45 (3):299-314.

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References found in this work

Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.

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