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CPAgame/prism and ultrafilters on Q and ω

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Języki publikacji
PL
Abstrakty
EN
In this paper we use the version CPAgame/prism of the Covering Property Axiom, which has been formulated by Ciesielski and Paw- likowski and holds in the iterated perfect set model, to study the rela- tions between different kinds of ultrafilters on ω and Q. In particular, we will give a full account for the logical relations between the properties of being a selective ultrafilter, a P-point, a Q-point, and an ω 1-OK point.
Wydawca
Rocznik
Strony
153--180
Opis fizyczny
Bibliogr. 15 poz.
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autor
Bibliografia
  • [1] Blass, A., Combinatorial characteristics of the continuum, in "Handbook of Set Theory", to appear.
  • [2] Bartoszyński, T., Judah, H., Set Theory. On the Structure of the Real Line, A. K. Peters Ltd, Wellesley, MA, 1995.
  • [3] Brodskii, M. L., On some properties of sets of positive measure (in Russian), Uspekhi Mat. Nauk (N. S.) 4, No. 3(31) (1949), 136-138.
  • [4] Ciesielski, K., Pawlikowski, J., Crowded and selective ultrafilters under the Covering Property Axiom, J. Appl. Anal. 9(1) (2003), 19-55.
  • [5] Ciesielski, K., Pawlikowski, J., Covering Property Axiom CPA, Cambridge Tracts in Math., Cambridge University Press, Cambridge, to appear.
  • [6] Coplakova, E., Hart, K. P., Crowded rational ultrafilters, Topology Appl. 97 (1999), 79-84.
  • [7] van Douwen, E. K., Better closed ultrafilters on Q, Topology Appl. 47 (1992), 173-177.
  • [8] Eggleston, H. G., Two measure properties of Cartesian product sets, Quart. J. Math. Oxford Ser. (2) 5 (1954), 108-115.
  • [9] Hart, K. P., Ultrafilters of character ω 1, J. Symbolic Logic 54(1) (1989)J 1-15.
  • [10] Jech, T., Set Theory, Academic Press, New York, 1978.
  • [11] Kunen, K., Weak P-points in N*, Colloq. Math. Soc. Janos Bolyai 23 (1978), Topology, Budapest (Hungary), 741-749.
  • [12] Laver, R., On the consistency of Borel's Conjecture, ActaMath. 137 (1976),151-169.
  • [13] Millan, A., A crowded Q-point under CPAgame/prism, Topology Proc. 29, (2005), 229-236.
  • [14] Miller, A. W ,. There are no Q-points in Laver's model for the Borel conjecture, Proc. Amer. Math. Soc. 78(1) (1980), 103-106.
  • [15] Wimmers, E. L., The Shelah P.point independence theorem, Israel J. Math. 43(1) (1982), 28-48.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD4-0002-0022
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