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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From accessible to inaccessible cardinals (Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones)
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...
On prime ideals of
Attilio Le Donne (1977)
Rendiconti del Seminario Matematico della Università di Padova
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Prime ideals yield almost maximal ideals
Andreas Blass (1987)
Fundamenta Mathematicae
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Topological representations of distributive lattices and Brouwerian logics
Marshall Harvey Stone (1938)
Časopis pro pěstování matematiky a fysiky
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The independence of the axiom of choice from the Boolean prime ideal theorem
J. Halperin (1964)
Fundamenta Mathematicae
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