PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2008 | 6 | 2 | 218-227
Tytuł artykułu

On the ideal (v 0)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The σ-ideal (v 0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v 0) to the family of Ramsey null sets. To describe add(v 0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v 0) = add(v 0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v 0) = ω 1 implies that (v 0) has the ideal type (c, ω 1, c).
Słowa kluczowe
Twórcy
Bibliografia
  • [1] Aniszczyk B., Remarks on σ-algebra of (s)-measurable sets, Bull. Polish Acad. Sci. Math., 1987, 35, 561–563
  • [2] Balcar B., Pelant J., Simon P., The space of ultrafilters on N covered by nowhere dense sets, Fund. Math., 1980, 110, 11–24
  • [3] Balcar B., Simon P., Disjoint refinement, In: Monk D., Bonnet R. (Eds.), Handbook of Boolean algebras, North-Holland, Amsterdam, 1989, 333–388
  • [4] Blass A., Combinatorial cardinal characteristics of the continuum, In: Foreman M., Magidor M., Kanamori A. (Eds.), Handbook of Set Theory, to appear
  • [5] Brendle J., Strolling through paradise, Fund. Math., 1995, 148, 1–25
  • [6] Brendle J., Halbeisen L., Löwe B., Silver measurability and its relation to other regularity properties, Math. Proc. Cambridge Philos. Soc., 2005, 138, 135–149 http://dx.doi.org/10.1017/S0305004104008187
  • [7] Di Prisco C., Henle J., Doughnuts floating ordinals square brackets and ultraflitters, J. Symbolic Logic, 2000, 65, 461–473 http://dx.doi.org/10.2307/2586548
  • [8] Engelking R., General topology, Mathematical Monographs, Polish Scientific Publishers, Warsaw, 1977
  • [9] Halbeisen L., Making doughnuts of Cohen reals, MLQ Math. Log. Q., 2003, 49, 173–178 http://dx.doi.org/10.1002/malq.200310016
  • [10] Hausdorff F., Summen von ℵ1 Mengen, Fund. Math., 1936, 26, 243–247
  • [11] Ismail M., Plewik Sz., Szymanski A., On subspaces of exp(N), Rend. Circ. Mat. Palermo, 2000, 49, 397–414 http://dx.doi.org/10.1007/BF02904253
  • [12] Kechris A., Classical descriptive set theory, Graduate Texts in Mathematics 156, Springer-Verlag, New York, 1995
  • [13] Kysiak M., Nowik A., Weiss T., Special subsets of the reals and tree forcing notions, Proc. Amer. Math. Soc., 2007, 135, 2975–2982 http://dx.doi.org/10.1090/S0002-9939-07-08808-9
  • [14] Louveau A., Une méthode topologique pour l’étude de la propriété de Ramsey, Israel J. Math., 1976, 23, 97–116 http://dx.doi.org/10.1007/BF02756789
  • [15] Louveau A., Simpson S., A separable image theorem for Ramsey mappings, Bull. Acad. Polon. Sci. Sér. Sci. Math., 1982, 30, 105–108
  • [16] Machura M., Cardinal invariants p, t and h and real functions, Tatra Mt. Math. Publ., 2004, 28, 97–108
  • [17] Moran G., Strauss D., Countable partitions of product spaces, Mathematika, 1980, 27, 213–224 http://dx.doi.org/10.1112/S002557930001010X
  • [18] Morgan J.C., Point set theory, Marcel Dekker, New York, 1990
  • [19] Nowik A., Reardon P., A dichotomy theorem for the Ellentuck topology, Real Anal. Exchange, 2003/04, 29, 531–542
  • [20] Pawlikowski J., Parametrized Ellentuck theorem, Topology Appl., 1990, 37, 65–73 http://dx.doi.org/10.1016/0166-8641(90)90015-T
  • [21] Plewik Sz., Ideals of nowhere Ramsey sets are isomorphic, J. Symbolic Logic, 1994, 59, 662–667 http://dx.doi.org/10.2307/2275415
  • [22] Plewik Sz., Voigt B., Partitions of reals: measurable approach, J. Combin. Theory Ser. A, 1991, 58, 136–140 http://dx.doi.org/10.1016/0097-3165(91)90079-V
  • [23] Rothberger F., On some problems of Hausdorff and of Sierpiński, Fund. Math., 1948, 35, 29–46
  • [24] Schilling K., Some category bases which are equivalent to topologies, Real Anal. Exchange, 1988/89, 14, 210–214
  • [25] Szpilrajn(Marczewski) E., Sur une classe de fonctions de M. Sierpiński et la classe correspondante d’ensambles, Fund. Math., 1935, 24, 17–34
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0021-0
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.