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Splitting families and the Noetherian type of βω / ω

Published online by Cambridge University Press:  12 March 2014

David Milovich
David Milovich*
Affiliation:
Mathematics Department, University of Wisconsin-Madison, Madison. Wisconsin., USA, E-mail: milovich@math.wisc.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1289 - 1306
Copyright
Copyright © Association for Symbolic Logic 2008

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