The independence of the axiom of choice from the Boolean prime ideal theorem
J. Halperin (1964)
Fundamenta Mathematicae
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Displaying similar documents to “A set-theoretical equivalent of the prime ideal theorem for Boolean algebras”
The independence of the axiom of choice from the Boolean prime ideal theorem
Remarks on Henkin's paper: Boolean representation trough, propositional calculus
J. Łoś (1957)
Fundamenta Mathematicae
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Effectiveness of the representation theory for Boolean algebras
J. Łoś, Czesław Ryll-Nardzewski (1955)
Fundamenta Mathematicae
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Prime Ideal Theorems and systems of finite character
Marcel Erné (1997)
Commentationes Mathematicae Universitatis Carolinae
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We study several choice principles for systems of finite character and prove their equivalence to the Prime Ideal Theorem in ZF set theory without Axiom of Choice, among them the Intersection Lemma (stating that if is a system of finite character then so is the system of all collections of finite subsets of meeting a common member of ), the Finite Cutset Lemma (a finitary version of the Teichm“uller-Tukey Lemma), and various compactness theorems. Several implications between these...
Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem
Eric Schechter (2006)
Fundamenta Mathematicae
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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.
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)
Collectanea Mathematica
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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.
Reduced direct products
T. Frayne, A. Morel, D. Scott (1962)
Fundamenta Mathematicae
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From accessible to inaccessible cardinals (Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones)
H. Keisler, Alfred Tarski (1964)
Fundamenta Mathematicae
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