Powers of transitive bases of measure and category
HTML articles powered by AMS MathViewer
- by Janusz Pawlikowski PDF
- Proc. Amer. Math. Soc. 93 (1985), 719-729 Request permission
Abstract:
We prove that on the real line the minimal cardinality of a base of measure zero sets equals the minimal cardinality of their transitive base. Next we show that it is relatively consistent that the minimal cardinality of a base of meager sets is greater than the minimal cardinality of their transitive base. We also prove that it is relatively consistent that the transitive additivity of measure zero sets is greater than the ordinary additivity and that the same is true about meager sets.References
- Tomek Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), no. 1, 209–213. MR 719666, DOI 10.1090/S0002-9947-1984-0719666-7
- Arnold W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), no. 1, 93–114. MR 613787, DOI 10.1090/S0002-9947-1981-0613787-2
- Arnold W. Miller, Additivity of measure implies dominating reals, Proc. Amer. Math. Soc. 91 (1984), no. 1, 111–117. MR 735576, DOI 10.1090/S0002-9939-1984-0735576-9
- Roman Sikorski, Boolean algebras, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 25, Springer-Verlag New York, Inc., New York, 1969. MR 0242724
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 719-729
- MSC: Primary 03E15; Secondary 03E35, 04A15, 28A05, 54A25
- DOI: https://doi.org/10.1090/S0002-9939-1985-0776210-2
- MathSciNet review: 776210