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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Normal filters generated by a family of sets


Authors: Carlos Augusto Di Prisco and Carlos Enrique Uzcategui
Journal: Proc. Amer. Math. Soc. 101 (1987), 513-518
MSC: Primary 04A20; Secondary 03E05
DOI: https://doi.org/10.1090/S0002-9939-1987-0908659-0
MathSciNet review: 908659
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Abstract: We study normal filters on the set spaces $ \lambda ,{\mathcal{P}_\kappa }\left( \lambda \right),{\left[ \lambda \right]^\kappa }$, and $ {\left( \lambda \right)^\kappa }$. We characterize the least normal $ \gamma $-complete filter containing a given $ \gamma $-complete filter for $ \gamma \geq {\omega _1}$. If $ \mathcal{F}$ is a $ {\omega _1}$-complete filter on any of the set spaces mentioned, the least $ {\omega _1}$-complete normal filter containing it is the filter generated by the sets $ \left\{ {x \in E\left\vert {{\alpha _1}, \ldots ,{\alpha _n} \in x \to x \in f\left( {{\alpha _1}, \ldots ,{\alpha _n}} \right)} \right.} \right\}$ where $ f:{\lambda ^{ < \omega }} \to \mathcal{F}$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908659-0
Article copyright: © Copyright 1987 American Mathematical Society