Displaying similar documents to “Prime ideals yield almost maximal ideals”

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 S is a system of finite character then so is the system of all collections of finite subsets of ⋃ S meeting a common member of S ), the Finite Cutset Lemma (a finitary version of the Teichm“uller-Tukey Lemma), and various compactness theorems. Several implications between these...