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Properties of ideals on the generalized Cantor spaces

Published online by Cambridge University Press:  12 March 2014

Jan Kraszewski
Jan Kraszewski*
Affiliation:
Institute of Mathematics, University of Wrocław, PL. Grunwaldzki 2/4. 50-156 Wrocław, Poland, E-mail: kraszew@math.uni.wroc.pl
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Abstract

We define a class of productiveσ-ideals of subsets of the Cantor space 2ω and observe that both σ-ideals of meagre sets and of null sets are in this class. From every productive σ-ideal we produce a σ-ideal of subsets of the generalized Cantor space 2κ. In particular, starting from meagre sets and null sets in 2ω we obtain meagre sets and null sets in 2ω, respectively. Then we investigate additivity, covering number, uniformity and cofinality of . For example, we show that

Our results generalizes those from [5].

Keywords

Cantor spaceσ-idealsnull setsmeagre setscardinal functions
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1303 - 1320
Copyright
Copyright © Association for Symbolic Logic 2001

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