Tukey order among F_σ ideals

2020/11/25 by Jialiang He, He, Jialiang, Michael Hrušák +5
Economics, Econometrics and Finance · Mathematics · #03E05 #03E15 #06A07 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Economic theories and models #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2011.13038

openalex publication_date 2020/11/25 · openalex created_date 2020/12/07 · openalex updated_date 2026/07/28

Abstract

We investigate the Tukey order in the class of F_σ ideals of subsets of ω. We show that no nontrivial F_σ ideal is Tukey below a G_δ 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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