Skip to main content
SpringerLink
Log in

On the ideal (v 0)

  • Research Article
  • Published:
Central European Journal of Mathematics

Abstract

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).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aniszczyk B., Remarks on σ-algebra of (s)-measurable sets, Bull. Polish Acad. Sci. Math., 1987, 35, 561–563

    MATH  MathSciNet  Google Scholar 

  2. Balcar B., Pelant J., Simon P., The space of ultrafilters on N covered by nowhere dense sets, Fund. Math., 1980, 110, 11–24

    MATH  MathSciNet  Google Scholar 

  3. Balcar B., Simon P., Disjoint refinement, In: Monk D., Bonnet R. (Eds.), Handbook of Boolean algebras, North-Holland, Amsterdam, 1989, 333–388

    Google Scholar 

  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

    MATH  MathSciNet  Google Scholar 

  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

    Article  MATH  MathSciNet  Google Scholar 

  7. Di Prisco C., Henle J., Doughnuts floating ordinals square brackets and ultraflitters, J. Symbolic Logic, 2000, 65, 461–473

    Article  MATH  MathSciNet  Google Scholar 

  8. Engelking R., General topology, Mathematical Monographs, Polish Scientific Publishers, Warsaw, 1977

    Google Scholar 

  9. Halbeisen L., Making doughnuts of Cohen reals, MLQ Math. Log. Q., 2003, 49, 173–178

    Article  MATH  MathSciNet  Google Scholar 

  10. Hausdorff F., Summen von ℵ1 Mengen, Fund. Math., 1936, 26, 243–247

    Google Scholar 

  11. Ismail M., Plewik Sz., Szymanski A., On subspaces of exp(N), Rend. Circ. Mat. Palermo, 2000, 49, 397–414

    Article  MATH  MathSciNet  Google Scholar 

  12. Kechris A., Classical descriptive set theory, Graduate Texts in Mathematics 156, Springer-Verlag, New York, 1995

    Google Scholar 

  13. Kysiak M., Nowik A., Weiss T., Special subsets of the reals and tree forcing notions, Proc. Amer. Math. Soc., 2007, 135, 2975–2982

    Article  MATH  MathSciNet  Google Scholar 

  14. Louveau A., Une méthode topologique pour l’étude de la propriété de Ramsey, Israel J. Math., 1976, 23, 97–116

    Article  MATH  MathSciNet  Google Scholar 

  15. Louveau A., Simpson S., A separable image theorem for Ramsey mappings, Bull. Acad. Polon. Sci. Sér. Sci. Math., 1982, 30, 105–108

    MATH  MathSciNet  Google Scholar 

  16. Machura M., Cardinal invariants p, t and h and real functions, Tatra Mt. Math. Publ., 2004, 28, 97–108

    MATH  MathSciNet  Google Scholar 

  17. Moran G., Strauss D., Countable partitions of product spaces, Mathematika, 1980, 27, 213–224

    Article  MATH  MathSciNet  Google Scholar 

  18. Morgan J.C., Point set theory, Marcel Dekker, New York, 1990

    MATH  Google Scholar 

  19. Nowik A., Reardon P., A dichotomy theorem for the Ellentuck topology, Real Anal. Exchange, 2003/04, 29, 531–542

    MathSciNet  Google Scholar 

  20. Pawlikowski J., Parametrized Ellentuck theorem, Topology Appl., 1990, 37, 65–73

    Article  MATH  MathSciNet  Google Scholar 

  21. Plewik Sz., Ideals of nowhere Ramsey sets are isomorphic, J. Symbolic Logic, 1994, 59, 662–667

    Article  MATH  MathSciNet  Google Scholar 

  22. Plewik Sz., Voigt B., Partitions of reals: measurable approach, J. Combin. Theory Ser. A, 1991, 58, 136–140

    Article  MATH  MathSciNet  Google Scholar 

  23. Rothberger F., On some problems of Hausdorff and of Sierpiński, Fund. Math., 1948, 35, 29–46

    MATH  MathSciNet  Google Scholar 

  24. Schilling K., Some category bases which are equivalent to topologies, Real Anal. Exchange, 1988/89, 14, 210–214

    MathSciNet  Google Scholar 

  25. Szpilrajn(Marczewski) E., Sur une classe de fonctions de M. Sierpiński et la classe correspondante d’ensambles, Fund. Math., 1935, 24, 17–34

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007, Katowice, Poland

    Piotr Kalemba, Szymon Plewik & Anna Wojciechowska

Authors
  1. Piotr Kalemba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Szymon Plewik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anna Wojciechowska
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Piotr Kalemba.

About this article

Cite this article

Kalemba, P., Plewik, S. & Wojciechowska, A. On the ideal (v 0). centr.eur.j.math. 6, 218–227 (2008). https://doi.org/10.2478/s11533-008-0021-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11533-008-0021-0

MSC

Keywords

Search

Navigation