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Transactions of the American Mathematical Society

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On two-cardinal properties of ideals

Author: Jacek Cichoń
Journal: Trans. Amer. Math. Soc. 314 (1989), 693-708
MSC: Primary 04A15; Secondary 03E35, 28A05
MathSciNet review: 1005527
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Abstract: We investigate two-cardinal properties of ideals. These properties involve notions such as Luzin sets, special coverings, etc. We apply our results to the ideals of meagre sets and of negligible sets in the real line. In case of the negligible sets, we relate these properties to caliber and precalibers of the measure algebra.

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  • [CKP] J. Cichoń, A. Kamburelis and J. Pawlikowski, On dense subsets of the measure algebra, Proc. Amer. Math. Soc. 94 (1985). MR 781072 (86j:04001)
  • [CP] J. Cichoń and J. Pawlikowski, On ideals of subsets of the plane and on Cohen reals, J. Symbolic Logic 51 (1986). MR 853839 (88b:03072)
  • [CSW] J. Cichoń, A Szymański and B. Weglorz, On families of sets of measure zero, Colloq. Math. 52 (1987).
  • [F] D. Fremlin, Cichon's diagram, Sem. d'Initiation a l'Analyse (G. Choquet, M. Rogalski, J. Saint-Raymond, eds.), no. 23, Univ. Pierre et Marie Curie, Paris, 1983-84.
  • [K] K. Kunen, Set theory. An Introduction to independence proofs, North-Holland, Amsterdam, 1980. MR 597342 (82f:03001)
  • [M] G. Mokobodzki, Ensembles à coupes denombrables et capacities domineé par une mesure, Université de Strasbourg, Séminaire de Probabilités, 1977/78.
  • [P] J. Pawlikowski, Why Solovay real produces a Cohen real, J. Symbolic Logic 51 (1986).
  • [T] J. Truss, On random and Cohen reals, J. Symbolic Logic 48 (1983). MR 727790 (85h:03055)

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Keywords: Set theory, ideal, Lebesgue measure, category, boolean algebras, cardinal numbers
Article copyright: © Copyright 1989 American Mathematical Society

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