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T. Frayne, A. Morel, D. Scott (1962)
Fundamenta Mathematicae
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T. Frayne, A. Morel, D. Scott (1962)
Fundamenta Mathematicae
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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...
J. Łoś, Czesław Ryll-Nardzewski (1955)
Fundamenta Mathematicae
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Stanley Wagon (1980)
Fundamenta Mathematicae
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J. Halperin (1964)
Fundamenta Mathematicae
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Marshall Harvey Stone (1938)
Časopis pro pěstování matematiky a fysiky
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