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

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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 . (a) If , then *U* is not -regular *iff U* has a least function *f* such that . (b) If and *U* is not -regular, then *U* has a least function.

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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