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Cofinalities of Borel ideals
Author(s) -
Hrušák Michael,
RojasRebolledo Diego,
Zapletal Jindřich
Publication year - 2014
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201200079
Subject(s) - cofinality , mathematics , invariant (physics) , ideal (ethics) , pairwise comparison , uncountable set , pure mathematics , discrete mathematics , countable set , epistemology , statistics , philosophy , mathematical physics
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 F σ ideal and prove a dichotomy for fragmented ideals. We show that every gradually fragmented ideal has cofinality consistently strictly smaller than the cardinal invariant b and produce a model where there are uncountably many pairwise distinct cofinalities of gradually fragmented ideals.