15 found
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  1.  2
    Forcing with Filters and Complete Combinatorics.Claude Laflamme - 1989 - Annals of Pure and Applied Logic 42 (2):125-163.
    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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  2.  24
    The Rudin-Blass Ordering of Ultrafilters.Claude Laflamme & Jian-Ping Zhu - 1998 - Journal of Symbolic Logic 63 (2):584-592.
    We discuss the finite-to-one Rudin-Keisler ordering of ultrafilters on the natural numbers, which we baptize the Rudin-Blass ordering in honour of Professor Andreas Blass who worked extensively in the area. We develop and summarize many of its properties in relation to its bounding and dominating numbers, directedness, and provide applications to continuum theory. In particular, we prove in ZFC alone that there exists an ultrafilter with no Q-point below in the Rudin-Blass ordering.
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  3.  9
    Consistency Results About Filters and the Number of Inequivalent Growth Types.Andreas Blass & Claude Laflamme - 1989 - Journal of Symbolic Logic 54 (1):50-56.
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  4.  13
    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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  5.  4
    Models with Second Order Properties V: A General Principle.Saharon Shelah, Claude Laflamme & Bradd Hart - 1993 - Annals of Pure and Applied Logic 64 (2):169-194.
    Shelah, S., C. Laflamme and B. Hart, Models with second order properties V: A general principle, Annals of Pure and Applied Logic 64 169–194. We present a general framework for carrying out the construction in [2-10] and others of the same type. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which would be much easier in a generic extension of the (...)
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  6.  1
    Bounding and Dominating Number of Families of Functions on Ω.Claude Laflamme - 1994 - Mathematical Logic Quarterly 40 (2):207-223.
    We pursue the study of families of functions on the natural numbers, with emphasis here on the bounded families. The situation being more complicated than the unbounded case, we attack the problem by classifying the families according to their bounding and dominating numbers, the traditional scheme for gaps. Many open questions remain.
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  7.  7
    Bartoszynski Tomek. On the Structure of Measurable Filters on a Countable Set. Real Analysis Exchange, Vol. 17 No. 2 , Pp. 681–701.Bartoszynski Tomek and Shelah Saharon. Intersection of Archive for Mathematical Logic, Vol. 31 , Pp. 221–226.Bartoszynski Tomek and Judah Haim. Measure and Category—Filters on Ω. Set Theory of the Continuum, Edited by Judah H., Just W., and Woodin H., Mathematical Sciences Research Institute Publications, Vol. 26, Springer-Verlag, New York, Berlin, Heidelberg, Etc., 1992, Pp. 175–201.Bartoszynski Tomek, Goldstern Martin, Judah Haim, and Shelah Saharon. All Meager Filters May Be Null. Proceedings of the American Mathematical Society, Vol. 117 , Pp. 515–521.Bartoszyński Tomek. Remarks on the Intersection of Filters. Topology and its Applications, Vol. 84 , Pp. 139–143. [REVIEW]Claude Laflamme - 2001 - Bulletin of Symbolic Logic 7 (3):388-389.
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  8.  11
    Bartoszynski Tomek. On the Structure of Measurable Filters on a Countable Set. Real Analysis Exchange, Vol. 17 No. 2 (1992), Pp. 681–701. Bartoszynski Tomek and Shelah Saharon. Intersection of Archive for Mathematical Logic, Vol. 31 (1992), Pp. 221–226. Bartoszynski Tomek and Judah Haim. Measure and Category—Filters on Ω. Set Theory of the Continuum, Edited by Judah H., Just W., and Woodin H., Mathematical Sciences Research Institute Publications, Vol. 26, Springer-Verlag, New York, Berlin, Heidelberg .. [REVIEW]Claude Laflamme - 2001 - Bulletin of Symbolic Logic 7 (3):388-389.
  9.  13
    Combinatorial Properties of Filters and Open Covers for Sets of Real Numbers.Claude Laflamme & Marion Scheepers - 1999 - Journal of Symbolic Logic 64 (3):1243-1260.
    We analyze combinatorial properties of open covers of sets of real numbers by using filters on the natural numbers. In fact, the goal of this paper is to characterize known properties related to ω-covers of the space in terms of combinatorial properties of filters associated with these ω-covers. As an example, we show that all finite powers of a set R of real numbers have the covering property of Menger if, and only if, each filter on ω associated with its (...)
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  10.  13
    Upward Directedness of the Rudin-Keisler Ordering of P-Points.Claude Laflamme - 1990 - Journal of Symbolic Logic 55 (2):449-456.
  11.  7
    On the Order Structure of the Hyperreal Line.William S. Hatcher & Claude Laflamme - 1983 - Mathematical Logic Quarterly 29 (4):197-202.
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  12.  4
    Montréal, Québec, Canada May 17–21, 2006.Jeremy Avigad, Sy Friedman, Akihiro Kanamori, Elisabeth Bouscaren, Philip Kremer, Claude Laflamme, Antonio Montalbán, Justin Moore & Helmut Schwichtenberg - 2007 - Bulletin of Symbolic Logic 13 (1).
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  13. REVIEWS-Five Papers.T. Bartoszynski & Claude Laflamme - 2001 - Bulletin of Symbolic Logic 7 (3):388-389.
     
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  14. [Omnibus Review].Claude Laflamme - 2001 - Bulletin of Symbolic Logic 7 (3):388-389.
  15. S. Todorcevic, Introduction to Ramsey Spaces.Claude Laflamme - 2011 - Bulletin of Symbolic Logic 17 (2):269.