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The cofinality of the strong measure zero ideal

Published online by Cambridge University Press:  12 March 2014

Teruyuki Yorioka
Affiliation:
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada-Ku, Kobe 657-8501, Japan, E-mail: yorioka@kurt.cla.kobe-u.ac.jp
Corresponding

Abstract

We give a characterization of the cofinality of the strong measure zero ideal under the continuum hypothesis and prove that we can force it to a value less than the power of the continuum.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

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References

[1]Bartoszyński, Tomek and Judah, Haim, Set theory: On the structure of the real line, A. K. Peters, Wellesley, Massachusetts, 1995.Google Scholar
[2]Borel, Emil, Sur la classification des ensembles de mesure nulle, Bulletin de la Société Mathématique de France, vol. 47 (1919), pp. 97125.CrossRefGoogle Scholar
[3]Kunen, Kenneth, Set theory: An introduction to independence proofs, Studies in Logic, vol. 102, North Holland, 1980.Google Scholar
[4]Seredeyński, Witold, Some operations related with translation, Colloquium Mathematicum, vol. 57 (1989), no. 2, pp. 203219.CrossRefGoogle Scholar
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