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On the role of the Baire category theorem and dependent choice in the foundations of logic. (English) Zbl 0567.03023

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.

MathOverflow Questions:

BCT equivalent to DC

MSC:

03E25 Axiom of choice and related propositions
06E10 Chain conditions, complete algebras
54E52 Baire category, Baire spaces
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References:

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