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Transactions of the American Mathematical Society

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



End extensions, conservative extensions, and the Rudin-Frolík ordering

Author: Andreas Blass
Journal: Trans. Amer. Math. Soc. 225 (1977), 325-340
MSC: Primary 02H13; Secondary 04A05
MathSciNet review: 0424556
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Abstract: The ordering of ultrafilters on the natural numbers defined by “E-prod N is an end extension of D-prod N,” the ordering defined by “E-prod N is a conservative extension of D-prod N,” and the Rudin-Frolik ordering are proved to be distinct if the continuum hypothesis holds. These three orderings are also characterized in terms of (not necessarily internal) ultrafilters in the Boolean algebra of internal sets of natural numbers in a nonstandard universe.

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Keywords: Ultrafilter, ultrapower, nonstandard model, Rudin-Keisler order, Rudin-Frolík order, elementary extensions, end extensions, conservative extensions
Article copyright: © Copyright 1977 American Mathematical Society