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Splitting families and the Noetherian type of βω / ω
Published online by Cambridge University Press: 12 March 2014
Abstract
Extending some results of Malykhin, we prove several independence results about base properties of βω / ω and its powers, especially the Noetherian type Nt(βω / ω), the least κ for which βω / ω has a base that is κ-like with respect to containment. For example, Nt(βω / ω) is at least s, but can consistently be ω1, c, c+, or strictly between ω1 and c. Nt(βω / ω) is also consistently less than the additivity of the meager ideal. Nt(βω / ω) is closely related to the existence of special kinds of splitting families.
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- Copyright © Association for Symbolic Logic 2008
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