TUKEY ORDER AMONG F-sigma IDEALS
JOURNAL OF SYMBOLIC LOGIC(2021)
摘要
We investigate the Tukey order in the class of F-sigma ideals of subsets of u. We show that no nontrivial F-sigma ideal is Tukey below a G(delta) 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 show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets.
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关键词
Tukey order, F-sigma ideal, flat ideal, gradually flat ideal
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