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The cofinality of cardinal invariants related to measure and category

Published online by Cambridge University Press:  12 March 2014

Tomek Bartoszynski
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Jaime I. Ihoda
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

Abstract

We prove that the following are consistent with ZFC:

1. 2ω = ω1 + #x039A;c = ω1 + ΚΒ = ΚU = ω2 (for measure and category simultaneously).

2. .

This concludes the discussion about the cofinality of Κc.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1989

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References

[BA1]Bartoszynski, T., Additivity of measure implies additivity of category, Transactions of the American Mathematical Society, vol. 281 (1984), pp. 209213.CrossRefGoogle Scholar
[Ba2]Bartoszynski, T., Combinatorial aspects of measure and category, Fundamenta Mathematicae, vol. 127 (1987), pp. 225239.CrossRefGoogle Scholar
[F]Fremlin, D., Cichoń's diagram, Séminaire d'initiation à l'analyse (G. Choquet–M. Rogalsi–J. Saint-Raymond), 23ème annee: 1983/1984, Université Pierre et Marie Curie (Paris-VI), Paris, 1984, Exposé 5.Google Scholar
[IhS]Ihoda, J. and Shelah, S., The Lebesgue measure and the Baire property: Laver's reals, preservation theorems for forcing, completing a chart of Kunen-Miller, Annals of Mathematics (submitted).Google Scholar
[Mi]Miller, A. W., Additivity of measure implies dominating reals, Proceedings of the American Mathematical Society, vol. 91 (1984), pp. 111117.CrossRefGoogle Scholar
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