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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
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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

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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