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On the role of the Baire Category Theorem and Dependent Choice in the foundations of logic

Published online by Cambridge University Press:  12 March 2014

Robert Goldblatt
Robert Goldblatt*
Affiliation:
Mathematics Department, Victoria University, Wellington, New Zealand
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 50 , Issue 2 , June 1985 , pp. 412 - 422
Copyright
Copyright © Association for Symbolic Logic 1985

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References

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