arXiv:0709.2436 Abstract | arXiv Analytics

arXiv:0709.2436 [math.LO]Abstract References Reviews Resources

A Note on Singular Cardinals in Set Theory Without Choice

Published 2007-09-15Version 1

We discuss how singular can cardinals be in absence of the axiom of choice. We show that, contrasting with known negative consistency results (of Gitik and others), certain positive results are provable. Then we pose some problems.

Comments: 29 pages, slides of a talk at the 13th International Congress of Logic, Methodology and Philosophy of Sciences (Beijing, August 9-15, 2007). The results were presented in 2005 at seminars of Moscow State University, Department of Mechanics and Mathematics

Categories: math.LO

Subjects: 03E25, 03E30, 03E35, 03E55

Keywords: set theory, singular cardinals, negative consistency results, positive results

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