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  1. Tukey order among ideals.Jialiang He, Michael Hrušák, Diego Rojas-Rebolledo & Sławomir Solecki - 2021 - Journal of Symbolic Logic 86 (2):855-870.
    We investigate the Tukey order in the class of Fσ ideals of subsets of ω. We show that no nontrivial Fσ ideal is Tukey below a Gδ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we (...)
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  • Towers in filters, cardinal invariants, and luzin type families.Jörg Brendle, Barnabás Farkas & Jonathan Verner - 2018 - Journal of Symbolic Logic 83 (3):1013-1062.
    We investigate which filters onωcan contain towers, that is, a modulo finite descending sequence without any pseudointersection. We prove the following results:Many classical examples of nice tall filters contain no towers.It is consistent that tall analytic P-filters contain towers of arbitrary regular height.It is consistent that all towers generate nonmeager filters, in particular Borel filters do not contain towers.The statement “Every ultrafilter contains towers.” is independent of ZFC.Furthermore, we study many possible logical implications between the existence of towers in filters, (...)
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