Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T17:14:34.119Z Has data issue: false hasContentIssue false
  • English
  • Français

The cofinality of cardinal invariants related to measure and category

Published online by Cambridge University Press:  12 March 2014

Tomek Bartoszynski ,
Jaime I. Ihoda  and
Saharon Shelah
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
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that the following are consistent with ZFC:

1. 2ω = ℵω1 + #x039A;c = ℵω1 + ΚΒ = ΚU = ω2 (for measure and category simultaneously).

2. .

This concludes the discussion about the cofinality of Κc.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 3 , September 1989 , pp. 719 - 726
Copyright
Copyright © Association for Symbolic Logic 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[BA1]Bartoszynski, T., Additivity of measure implies additivity of category, Transactions of the American Mathematical Society, vol. 281 (1984), pp. 209–213.CrossRefGoogle Scholar
[Ba2]Bartoszynski, T., Combinatorial aspects of measure and category, Fundamenta Mathematicae, vol. 127 (1987), pp. 225–239.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. 111–117.CrossRefGoogle Scholar