Ideal convergence of bounded sequences

Journal of Symbolic Logic 72 (2):501-512 (2007)

Abstract
We generalize the Bolzano-Weierstrass theorem on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family
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DOI 10.2178/jsl/1185803621
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Analytic Ideals and Their Applications.Sławomir Solecki - 1999 - Annals of Pure and Applied Logic 99 (1-3):51-72.
Separation Properties of Ideals Over Ω.Winfried Just & Žarko Mijajlović - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (3):267-276.

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