More Cofinal Types of Definable Directed Orders
نویسنده
چکیده
We study the cofinal diversity of analytic p-ideals and analytic relative σ-ideals of compact sets. We prove that the σ-ideal of compact meager sets is not cofinally simpler than the asymptotic density zero ideal; this concludes the study of the cofinal types of classical analytic ideals. We obtain this result by using a Ramsey-type partition calculus, which allows us to capture the relevant combinatorial properties of our ideals. We also show that the structure (P(ω),⊆?) embeds into the family of Fσ p-ideals on ω and into the family of monotone σ-ideals of compact sets, partially ordered by Tukey reducibility. To this end, we introduce a general construction scheme for lower semicontinuous submeasures, and we carry out a detailed analysis of the combinatorial properties of monotone σ-ideals of compact
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Cofinal Types of Topological Directed Orders
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