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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Limits in the uniform ultrafilters


Authors: Joni Baker and Kenneth Kunen
Journal: Trans. Amer. Math. Soc. 353 (2001), 4083-4093
MSC (2000): Primary 54D80, 54D40
DOI: https://doi.org/10.1090/S0002-9947-01-02843-4
Published electronically: May 22, 2001
MathSciNet review: 1837221
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Abstract:

Let $u(\kappa)$ be the space of uniform ultrafilters on $\kappa$. If $\kappa$ is regular, then there is an $\mathbf x \in u(\kappa)$which is not an accumulation point of any subset of $u(\kappa)$ of size $\kappa$ or less. $\mathbf x$ is also good, in the sense of Keisler.


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Additional Information

Joni Baker
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 57306
Email: baker@math.wisc.edu

Kenneth Kunen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 57306
Email: kunen@math.wisc.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02843-4
Keywords: Weak $P$-point, good ultrafilter, mediocre point
Received by editor(s): September 18, 2000
Received by editor(s) in revised form: March 21, 2001
Published electronically: May 22, 2001
Additional Notes: Both authors’ work was partly supported by NSF Grant DMS-9704520. They wish to thank the referee for a number of useful comments.
Article copyright: © Copyright 2001 American Mathematical Society