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Transactions of the American Mathematical Society
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
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0351822-6
PII: S 0002-9947(1974)0351822-6
Keywords: Ultrafilters, P-points, Ramsey ultrafilters, ultrapowers, Dedekind cuts
Article copyright: © Copyright 1974 American Mathematical Society