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After all, there are some inequalities which are provable in ZFC

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

Abstract

We address ZFC inequalities between some cardinal invariants of the continuum, which turned out to be true in spite of strong expectations given by [11].

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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, Massachusetts, 1995.
[4]Bartoszyński, Tomek, Rosłanowski, Andrzej, and Shelah, Saharon, Adding one random real, This Journal, vol. 61 (1996), pp. 8090.
[5]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.
[6]Jech, Thomas, Set theory, Academic Press, New York, 1978.
[7]Krawczyk, Adam, Dominating reals add random reals, unpublished notes, 1985.
[8]Miller, Arnold W., Some properties of measure and category, Transactions of the American Mathematical Society, vol 266 (1981), no. 1, pp. 93114.
[9]Pawlikowski, Janusz, Why Solovay real produces Cohen real, This Journal, vol. 51 (1986), no. 4, pp. 957968.
[10]Rosłanowski, Andrzej and Shelah, Saharon, Localizations of infinite subsets of ω, Archive for Mathematical Logic, vol. 35 (1996), pp. 315339.
[11]Rosłanowski, Andrzej and Shelah, Saharon, Norms on possibilities I: forcing with trees and creatures, Memoirs of the American Mathematical Society, vol. 114 (1999), no. 671.
[12]Shelah, Saharon, Proper and improper forcing, Perspectives in Logic, Springer Verlag, 1998.

After all, there are some inequalities which are provable in ZFC

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

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