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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 $P_ \kappa \lambda$


Author: Masahiro Shioya
Journal: Proc. Amer. Math. Soc. 123 (1995), 1565-1572
MSC: Primary 04A20
DOI: https://doi.org/10.1090/S0002-9939-1995-1234632-6
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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Keywords: <!โ€“ MATH ${P_\kappa }\lambda$ โ€“> <IMG WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="${P_\kappa }\lambda$">, <!โ€“ MATH $CF_{\kappa \lambda }^\mu$ โ€“> <IMG WIDTH="54" HEIGHT="42" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$CF_{\kappa \lambda }^\mu$">, <!โ€“ MATH $SCF_{\kappa \lambda }^\mu$ โ€“> <IMG WIDTH="67" HEIGHT="42" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$SCF_{\kappa \lambda }^\mu$">
Article copyright: © Copyright 1995 American Mathematical Society