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

Blass, Andreas

doi:10.1090/S0002-9947-1977-0424556-X

End extensions, conservative extensions, and the Rudin-Frolík ordering
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Trans. Amer. Math. Soc. 225 (1977), 325-340 Request permission

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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