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 “Two theorems of functional analysis effectively equivalent to choice axioms”
The independence of the axiom of choice from 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.
Partially additive states on orthomodular posets
Josef Tkadlec (1991)
Colloquium Mathematicae
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We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which respect the ordering and the orthocomplementation in P and which are additive on B. We call such functions B-states on P. We first show that every P possesses "enough" two-valued B-states. This improves the main result in [13], where B is the centre of P. Moreover, it allows us to construct a closure-space representation of orthomodular lattices. We do this in the third section. This result...
A geometric form of the axiom of choice
J. Bell, David Fremlin (1972)
Fundamenta Mathematicae
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The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
G. Gardiner (1974)
Fundamenta Mathematicae
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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.
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...