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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10.1016/0168-0072(89)90052-3

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Citations of this work

A long chain of P-points.Borisa Kuzeljevic & Dilip Raghavan - 2018 - Journal of Mathematical Logic 18 (1):1850004.
Canjar Filters.Osvaldo Guzmán, Michael Hrušák & Arturo Martínez-Celis - 2017 - Notre Dame Journal of Formal Logic 58 (1):79-95.

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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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