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The covering number and the uniformity of the ideal ℐf

✍ Scribed by Noboru Osuga

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
162 KB
Volume
52
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

Let f, g ∈ ^ω^ ω . We will denote by g ≫ f that for every k < ω, f (n ^k^ ) ≤ g (n ) except for finitely many n . The ideal ℐ~f~ on ^ω^ 2 is the collection of sets X such that, for some g ≫ f and τ ∈ ∏~n <ω~ ^g (n )^2, every x ∈ X satisfies τ (n ) ⊂ x for infinitely many n . In the present paper, we will prove the consistency of cov(ℐ~f~ ) < 𝔠 and non(ℐ~f~ ) < 𝔠. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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