Properties of ideals on the generalized Cantor spaces

Journal of Symbolic Logic 66 (3):1303-1320 (2001)
Abstract
We define a class of productive σ-ideals of subsets of the Cantor space 2 ω and observe that both σ-ideals of meagre sets and of null sets are in this class. From every productive σ-ideal I we produce a σ-ideal I κ , of subsets of the generalized Cantor space 2 κ . In particular, starting from meagre sets and null sets in 2 ω we obtain meagre sets and null sets in 2 κ , respectively. Then we investigate additivity, covering number, uniformity and cofinality of I κ . For example, we show that non(I = non(I ω 1 ) = non(I ω 2 ). Our results generalizes those from [5]
Keywords Cantor Space   $\sigma$-Ideals   Null Sets   Meagre Sets   Cardinal Functions
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