Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T01:39:54.268Z Has data issue: false hasContentIssue false
  • English
  • Français

Combinatorial properties of the ideal ℬ2

Published online by Cambridge University Press:  12 March 2014

J. Cichoń ,
A. Rosłanowski ,
J. Steprans  and
B. Wȩglorz
J. Cichoń
Affiliation:
Institute of Mathematics, University of Wroclaw, 50-484 Wroclaw, Poland
A. Rosłanowski
Affiliation:
Institute of Mathematics, University of Wroclaw, 50-484 Wroclaw, Poland
J. Steprans
Affiliation:
Department of Mathematics, York University, Ontario M3J IP3, Canada
B. Wȩglorz
Affiliation:
Institute of Mathematics, University of Wroclaw, 50-484 Wroclaw, Poland
Get access Rights & Permissions [Opens in a new window]

Abstract

By ℬ2 we denote the σ-ideal of all subsets A of the Cantor set {0, 1}ω such that for every infinite subset T of ω the restriction A∣{0, 1}T is a proper subset of {0, 1}T. In this paper we investigate set theoretical properties of this and similar ideals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 1 , March 1993 , pp. 42 - 54
Copyright
Copyright © Association for Symbolic Logic 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[ARS]Abraham, U., Rubin, M., and Shelah, S., On the consistency of some partition theorems for continuous colorings and the structure of ω 1-dense real order types, Annals of Pure and Applied Logic, vol. 29 (1985), pp. 123–206.CrossRefGoogle Scholar
[B]Baumgartner, J. E., Iterated forcing. Proceedings of the Summer School in Set Theory (Mathias, A. R. D., editor), Cambridge University Press, London and New York, 1978.Google Scholar
[FR]Fremlin, D., On Cichoń's diagram, Sem. d'Initiation a l'Analyse (Choquet, G., Rogalski, M., and Saint-Raymond, J., editors), no. 23, Univ. Pierre et Marie Curie, Paris, 1983–84.Google Scholar
[L]Laver, R., On the consistency of Borel's conjecture, Acta Mathematica, vol. 137 (1976), pp. 151–169.CrossRefGoogle Scholar
[M]Mycielski, J., Some new ideals of subsets on the real line, Colloquium Mathematicum, vol. 20 (1969), pp. 71–76.CrossRefGoogle Scholar
[Ma]Mathias, A. R. D., Happy families, Annals of Mathematical Logic, vol. 12 (1977), pp. 59–111.CrossRefGoogle Scholar
[Mi]Miller, A. W., Rational perfect set forcing, Contemporary Mathematics, vol. 31 (1984), pp. 143–159.CrossRefGoogle Scholar
[R]Rosłanowski, A., On Game Ideals, Colloquium Mathematicum, vol. 59 (1990), pp. 159–168.CrossRefGoogle Scholar
[S]Shelah, S., Proper Forcing, Lecture Notes in Mathematics vol. 940, Springer-Verlag, Heidelberg, 1982.CrossRefGoogle Scholar