Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 

 

Weakly normal filters and irregular ultrafilters


Author: A. Kanamori
Journal: Trans. Amer. Math. Soc. 220 (1976), 393-399
MSC: Primary 04A20; Secondary 02K35
DOI: https://doi.org/10.1090/S0002-9947-1976-0480041-X
MathSciNet review: 0480041
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a filter over a regular cardinal, least functions and the consequent notion of weak normality are described. The following two results, which make a basic connection between the existence of least functions and irregularity of ultrafilters, are then proved: Let U be a uniform ultrafilter over a regular cardinal $ \kappa $. (a) If $ \kappa = {\lambda ^ + }$, then U is not $ (\lambda ,{\lambda ^ + })$-regular iff U has a least function f such that $ \{ \xi < {\lambda ^ + }\vert{\text{cf}}(f(\xi )) = \lambda \} \in U$. (b) If $ \omega \leqslant \mu < \kappa $ and U is not $ (\omega ,\mu )$-regular, then U has a least function.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 04A20, 02K35

Retrieve articles in all journals with MSC: 04A20, 02K35


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0480041-X
Keywords: Least functions, weakly normal filters, regularity of uniform ultrafilters
Article copyright: © Copyright 1976 American Mathematical Society