Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-25T12:27:45.094Z Has data issue: false hasContentIssue false

The covering numbers of Mycielski ideals are all equal

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel, E-mail: shelah@math.huji.ac.il
Juris Steprāns
Affiliation:
Department of Mathematics, York University, 4700 Keele Street, Toronto Ontario, CanadaM3J 1P3, E-mail:steprans@mathstat.yorku.ca

Abstract

The Mycielski ideal is defined to consist of all sets Ak such that {fX : fA} ≠ Xk for all . It will be shown that the covering numbers for these ideals are all equal. However, the covering numbers of the closely associated Rosłanowski ideals will be shown to be consistently different.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2001

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

[1]Balcerzak, Marek, Typical properties of continuous functions via the Vietoris topology. Real Analysis Exchange, vol. 18 (1992/1993), no. 2, pp. 532536.CrossRefGoogle Scholar
[2]Balcerzak, Marek and Rosłanowski, Andrzej, On Mycielski ideals, Proceedings ofthe American Mathematical Society, vol. 110 (1990), no. 1, pp. 243250.CrossRefGoogle Scholar
[3]Cichoń, J., Rosłanowski, A., J. Steprāns, and Wȩglorz, B., Combinatorial properties of the ideal ƥ2, this Journal, vol. 58 (1993), no. 1, pp. 4254.Google Scholar
[4]Hejduk, Jacek, Convergence with respect to the Mycielski σ-ideal, Demonstratio Mathematica, vol. 22 (1989), no. 1, pp. 4350.CrossRefGoogle Scholar
[5]Kamo, Shizuo, Some remarks about Mycielski ideals, Colloquium Mathematicum, vol. 65 (1993), no. 2, pp. 291299.CrossRefGoogle Scholar
[6]Mycielski, Jan, Some new ideals of sets on the real line, Colloquium Mathematicum, vol. 20 (1969), pp. 7176.CrossRefGoogle Scholar
[7]Plewik, Szymon, On some problem of A. Roslanowski, Colloquium Mathematicum, vol. 69 (1995), no. 2, pp. 297298.CrossRefGoogle Scholar
[8]Roslanowski, A., Mycielski ideals generated by uncountable systems, Colloquium Mathematicum, vol. 66 (1994), no. 2, pp. 187200.CrossRefGoogle Scholar
[9]Rosłanowski, Andrzej, On game ideals, Colloquium Mathematicum, vol. 59 (1990), no. 2, pp. 159168.CrossRefGoogle Scholar
[10]Schilling, Kenneth, A category base for Mycielski's ideals, Real Analysis Exchange, vol. 19 (1993/1994), no. 1, pp. 98105.CrossRefGoogle Scholar
[11]Sharp, James D. and Thomas, Simon, Uniformization problems and the cofinalily of the infinite symmetric group, Notre Dame Journal of Formal Logic, vol. 35 (1994), no. 3, pp. 328345.CrossRefGoogle Scholar