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The Journal of Symbolic Logic The Journal of Symbolic Logic

Article contents

Adding one random real

Published online by Cambridge University Press:  12 March 2014

Tomek Bartoszyński ,
Andrzej Rosłanowski  and
Saharon Shelah
Tomek Bartoszyński
Affiliation:
Department of Mathematics, Boise State University, Boise, Idaho 83725, USA, E-mail: tomek@math.idbsu.edu
Andrzej Rosłanowski
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel, E-mail: roslanow@sunrise.huji.ac.il Mathematical Institute, Wroclaw University, Wroclaw, Poland, E-mail: roslanow@sunrise.huji.ac.il
Saharon Shelah
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel, E-mail: shelah@sunrise.huji.ac.il
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Abstract

We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions may be large while the covering for measure is small.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 80 - 90
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Bartoszyński, Tomek, Additivity of measure implies additivity of category, Transactions of the American Mathematical Society, vol. 281 (1984), no. 1, pp. 209–213.CrossRefGoogle Scholar
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[4]Fremlin, David H., Cichoń's diagram, no. 5, p. 13, presented at the Séminaire Initiation à l'Analyse, G. Choquet, M. Rogalski, J. Saint Raymond, at the Université Pierre et Marie Curie, Paris, 23e année., 1983/1984.Google Scholar
[5]Krawczyk, Adam, Dominating reals add random reals, unpublished notes, 1985.Google Scholar
[6]Miller, Arnold W., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), no. 1, pp. 93–114.CrossRefGoogle Scholar
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[8]Shelah, Saharon, Norms on possibilities, in preparation.Google Scholar
[9]Shelah, Saharon, Proper and Improper forcing, to appear, 199?Google Scholar
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