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  1. (1 other version)A few special ordinal ultrafilters.Claude Laflamme - 1996 - Journal of Symbolic Logic 61 (3):920-927.
    We prove various results on the notion of ordinal ultrafilters introduced by J. Baumgartner. In particular, we show that this notion of ultrafilter complexity is independent of the more familiar Rudin-Keisler ordering.
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  • (1 other version)Ultrafilters on ω.James E. Baumgartner - 1995 - Journal of Symbolic Logic 60 (2):624-639.
    We study the I-ultrafilters on ω, where I is a collection of subsets of a set X, usually R or ω 1 . The I-ultrafilters usually contain the P-points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.
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  • Ultrafilters on the natural numbers.Christopher Barney - 2003 - Journal of Symbolic Logic 68 (3):764-784.
    We study the problem of existence and generic existence of ultrafilters on ω. We prove a conjecture of $J\ddot{o}rg$ Brendle's showing that there is an ultrafilter that is countably closed but is not an ordinal ultrafilter under CH. We also show that Canjar's previous partial characterization of the generic existence of Q-points is the best that can be done. More simply put, there is no normal cardinal invariant equality that fully characterizes the generic existence of Q-points. We then sharpen results (...)
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  • P-hierarchy on β ω.Andrzej Starosolski - 2008 - Journal of Symbolic Logic 73 (4):1202-1214.
    We classify ultrafilters on ω with respect to sequential contours (see [4].[5]) of different ranks. In this way we obtain an ω1 sequence {Pα}1≤α≤ω1 of disjoint classes. We prove that non-emptiness of Pα for successor α ≥ 2 is equivalent to the existence of P-point. We investigate relations between P-hierarchy and ordinal ultrafilters (introduced by J. E. Baumgartner in [1]), we prove that it is relatively consistent with ZFC that the successor classes (for α ≥ 2) of P-hierarchy and ordinal (...)
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  • (1 other version)Ultrafilters on $omega$.James E. Baumgartner - 1995 - Journal of Symbolic Logic 60 (2):624-639.
    We study the $I$-ultrafilters on $\omega$, where $I$ is a collection of subsets of a set $X$, usually $\mathbb{R}$ or $\omega_1$. The $I$-ultrafilters usually contain the $P$-points, often as a small proper subset. We study relations between $I$-ultrafilters for various $I$, and closure of $I$-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether $I$-ultrafilters always exist.
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  • Free Boolean algebras and nowhere dense ultrafilters.Aleksander Błaszczyk - 2004 - Annals of Pure and Applied Logic 126 (1-3):287-292.
    An analogue of Mathias forcing is studied in connection of free Boolean algebras and nowhere dense ultrafilters. Some applications to rigid Boolean algebras are given.
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