Axioms which imply GCH
Jan Mycielski (2003)
Fundamenta Mathematicae
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We propose some new set-theoretic axioms which imply the generalized continuum hypothesis, and we discuss some of their consequences.
Jan Mycielski (2003)
Fundamenta Mathematicae
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We propose some new set-theoretic axioms which imply the generalized continuum hypothesis, and we discuss some of their consequences.
Ben Chad, Robin Knight, Rolf Suabedissen (2009)
Fundamenta Mathematicae
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A two-point set is a subset of the plane which meets every line in exactly two points. By working in models of set theory other than ZFC, we demonstrate two new constructions of two-point sets. Our first construction shows that in ZFC + CH there exist two-point sets which are contained within the union of a countable collection of concentric circles. Our second construction shows that in certain models of ZF, we can show the existence of two-point sets without explicitly invoking the...
Marcin Zieliński (2019)
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
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The results of Zarzycki for the cardinality of the sets of all bijections, surjections, and injections are generalized to the case when the domains and codomains are infinite and different. The elementary proofs the cardinality of the sets of bijections and surjections are given within the framework of the Zermelo-Fraenkel set theory with the axiom of choice. The case of the set of all injections is considered in detail and more explicit an expression is obtained when the Generalized...
A. Lévy (1964)
Fundamenta Mathematicae
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J. Henle, William Zwicker (1981)
Fundamenta Mathematicae
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Giorgio Venturi, Matteo Viale (2018)
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
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In this article we review the present situation in the foundations of set theory, discussing two programs meant to overcome the undecidability results, such as the independence of the continuum hypothesis; these programs are centered, respectively, on forcing axioms and Woodin's V = Ultimate-L conjecture. While doing so, we briefly introduce the key notions of set theory.
M. Jelić (1990)
Matematički Vesnik
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K. Wiśniewski (1972)
Fundamenta Mathematicae
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Kenneth Kunen, Franklin Tall (1979)
Fundamenta Mathematicae
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Alexander Abian, Paula Kemp (1992)
Publications de l'Institut Mathématique
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P. Andrews (1963)
Fundamenta Mathematicae
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J. Kelley (1950)
Fundamenta Mathematicae
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Nancy Moler, Patrick Suppes (1968)
Compositio Mathematica
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Perry Smith (1982)
Publications de l'Institut Mathématique
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