Concerning a proof of without axiom of choice
Petr Vopěnka (1965)
Commentationes Mathematicae Universitatis Carolinae
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Displaying similar documents to “Concerning a proof of without axiom of choice: A correction”
Concerning a proof of without axiom of choice
Inaccessible cardinals without the axiom of choice
Andreas Blass, Ioanna M. Dimitriou, Benedikt Löwe (2007)
Fundamenta Mathematicae
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We consider four notions of strong inaccessibility that are equivalent in ZFC and show that they are not equivalent in ZF.
Model in which is limit number
Karel Hrbáček (1965)
Commentationes Mathematicae Universitatis Carolinae
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On the Leibniz-Mycielski axiom in set theory
Ali Enayat (2004)
Fundamenta Mathematicae
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Motivated by Leibniz’s thesis on the identity of indiscernibles, Mycielski introduced a set-theoretic axiom, here dubbed the Leibniz-Mycielski axiom LM, which asserts that for each pair of distinct sets x and y there exists an ordinal α exceeding the ranks of x and y, and a formula φ(v), such that satisfies φ(x) ∧¬ φ(y). We examine the relationship between LM and some other axioms of set theory. Our principal results are as follows: 1. In the presence of ZF, the following are equivalent: (a)...
The Wholeness Axioms and the Class of Supercompact Cardinals
Arthur W. Apter (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.