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Cofinalities of Borel ideals

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Abstract

We study the possible values of the cofinality invariant for various Borel ideals on the natural numbers. We introduce the notions of a fragmented and gradually fragmented inline image ideal and prove a dichotomy for fragmented ideals. We show that every gradually fragmented ideal has cofinality consistently strictly smaller than the cardinal invariant inline image and produce a model where there are uncountably many pairwise distinct cofinalities of gradually fragmented ideals.

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