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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Powers of transitive bases of measure and category


Author: Janusz Pawlikowski
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0776210-2
Article copyright: © Copyright 1985 American Mathematical Society