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Proceedings of the American Mathematical Society

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

 

 

The minimal normal $ \mu$-complete filter on $ P\sb \kappa\lambda$


Author: Masahiro Shioya
Journal: Proc. Amer. Math. Soc. 123 (1995), 1565-1572
MSC: Primary 04A20
MathSciNet review: 1234632
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Abstract: We introduce the closed (resp. strongly closed) $ \mu $-unbounded filter $ CF_{\kappa \lambda }^\mu $ (resp. $ SCF_{\kappa \lambda }^\mu $) for a regular cardinal $ \mu \leq \kappa $, which is a $ \mu $-complete analog of the closed (resp. strongly closed) unbounded filter on $ {P_\kappa }\lambda $. We give their simple characterizations for the case $ \mu = {\omega _1}$. We also study generators of $ CF_{\kappa \lambda }^\nu $ (resp. $ SCF_{\kappa \lambda }^\nu $) over $ CF_{\kappa \lambda }^\mu $ (resp. $ SCF_{\kappa \lambda }^\mu $) for the case $ \omega < \mu < \nu $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1234632-6
Keywords: $ {P_\kappa }\lambda$, $ CF_{\kappa \lambda }^\mu$, $ SCF_{\kappa \lambda }^\mu $
Article copyright: © Copyright 1995 American Mathematical Society