Mycielski ideals generated by uncountable systems

Andrzej Roslanowski  

We generalize Mycielski ideals getting a large family of $\sigma$-ideals of subsets of $2^\omega$. Each ideal in the family is determined by a collection of elements of $[\omega]^\omega$ - so called generating system. We study the relations between the ideals generated by different systems and between these ideals and the classical ideals: the null ideal and the meager ideal. Further we investigate dependence of cardinal invariants of Mycielski ideals on the generating systems.

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