Properties of Ideals on The Generalized Cantor Spaces

We define a class of productive σ−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 J we produce a σ−ideal Jκ 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 2κ, respectively. Then we investigate additivity, covering number, uniformity and cofinality of Jκ. For example, we show that non(J ) = non(Jω1 ) = non(Jω2 ). Our results generalizes those from [5].