Forcing with filters and complete combinatorics

Annals of Pure and Applied Logic 42 (2):125-163 (1989)
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Abstract

We study ultrafilters produced by forcing, obtaining different combinatorics and related Rudin-Keisler ordering; in particular we answer a question of Baumgartner and Taylor regarding tensor products of ultrafilters. Adapting a method of Blass and Mathias, we show that in most cases the combinatorics satisfied by the ultrafilters recapture the forcing notion in the Lévy model

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References found in this work

Happy Families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Ultrafilters on a Countable Set.David Booth - 1970 - Annals of Mathematical Logic 2 (1):1.
Selective Ultrafilters and Homogeneity.Andreas Blass - 1988 - Annals of Pure and Applied Logic 38 (3):215-255.
Some Initial Segments of the Rudin-Keisler Ordering.Andreas Blass - 1981 - Journal of Symbolic Logic 46 (1):147-157.

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