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Adding one random real

  • Tomek Bartoszyński (a1), Andrzej Rosłanowski (a2) (a3) and Saharon Shelah (a4)

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.

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[1]Bartoszyński, Tomek, Additivity of measure implies additivity of category, Transactions of the American Mathematical Society, vol. 281 (1984), no. 1, pp. 209213.
[2]Bartoszyński, Tomek, Combinatorial aspects of measure and category, Fundamenta Mathematicae, vol. 127 (1987), no. 3, pp. 225239.
[3]Bartoszyński, Tomek and Judah, Haim, Set theory: the structure of the real line, A K Peters, Wellesley, MA, USA, 1995.
[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.
[5]Krawczyk, Adam, Dominating reals add random reals, unpublished notes, 1985.
[6]Miller, Arnold W., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), no. 1, pp. 93114.
[7]Pawlikowski, Janusz, Why Solovay real produces Cohen real, this Journal, vol. 51 (1986), no. 4, pp. 957968.
[8]Shelah, Saharon, Norms on possibilities, in preparation.
[9]Shelah, Saharon, Proper and Improper forcing, to appear, 199?

Adding one random real

  • Tomek Bartoszyński (a1), Andrzej Rosłanowski (a2) (a3) and Saharon Shelah (a4)

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