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December 2008 Splitting families and the Noetherian type of β ω ∖ ω
David Milovich
J. Symbolic Logic 73(4): 1289-1306 (December 2008). DOI: 10.2178/jsl/1230396919

Abstract

Extending some results of Malykhin, we prove several independence results about base properties of $\beta\omega\setminus\omega$ and its powers, especially the Noetherian type $Nt(\beta\omega\setminus\omega)$, the least $\kappa$ for which $\beta\omega\setminus\omega$ has a base that is $\kappa$-like with respect to containment. For example, $Nt(\beta\omega\setminus\omega)$ is at least 𝔰, consistently be $\omega_1$, 𝔠, 𝔠⁺, or strictly between $\omega_1$ and 𝔠. $Nt(\beta\omega\setminus\omega)$ is also consistently less than the additivity of the meager ideal. $Nt(\beta\omega\setminus\omega)$ is closely related to the existence of special kinds of splitting families.

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David Milovich. "Splitting families and the Noetherian type of β ω ∖ ω." J. Symbolic Logic 73 (4) 1289 - 1306, December 2008. https://doi.org/10.2178/jsl/1230396919

Information

Published: December 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1156.03049
MathSciNet: MR2467217
Digital Object Identifier: 10.2178/jsl/1230396919

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 4 • December 2008
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