Two theorems of functional analysis effectively equivalent to choice axioms
D. Edwards (1975)
Fundamenta Mathematicae
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Displaying similar documents to “The equivalence of Boolean prime ideal theorem and a theorem of functional analysis”
Two theorems of functional analysis effectively equivalent to choice axioms
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A geometric form of the axiom of choice
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The Tychonoff product theorem for compact Hausdorff spaces does not imply the axiom of choice: A new Proof. equivalent propositions.
B. R. Salinas, F. Bombal (1973)
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The independence of the axiom of choice from the Boolean prime ideal theorem
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A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
Miroslav Repický (2015)
Commentationes Mathematicae Universitatis Carolinae
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We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.
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Remarks on Henkin's paper: Boolean representation trough, propositional calculus
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Roman Sikorski (1948)
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Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem
Eric Schechter (2006)
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The principle that "any product of cofinite topologies is compact" is equivalent (without appealing to the Axiom of Choice) to the Boolean Prime Ideal Theorem.