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)



Ultrafilter mappings and their Dedekind cuts

Author: Andreas Blass
Journal: Trans. Amer. Math. Soc. 188 (1974), 327-340
MSC: Primary 04A20
MathSciNet review: 0351822
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let D be an ultrafilter on the set N of natural numbers. To each function $ p:N \to N$ and each ultrafilter E that is mapped to D by p, we associate a Dedekind cut in the ultrapower D-prod N. We characterize, in terms of rather simple closure conditions, the cuts obtainable in this manner when various restrictions are imposed on E and p. These results imply existence theorems, some known and some new, for various special kinds of ultrafilters and maps.

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

Similar Articles

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

Retrieve articles in all journals with MSC: 04A20

Additional Information

Keywords: Ultrafilters, P-points, Ramsey ultrafilters, ultrapowers, Dedekind cuts
Article copyright: © Copyright 1974 American Mathematical Society