Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T09:29:19.743Z Has data issue: false hasContentIssue false
  • English
  • Français

Additivity properties of topological diagonalizations

Published online by Cambridge University Press:  12 March 2014

Tomek Bartoszynski ,
Saharon Shelah  and
Boaz Tsaban
Tomek Bartoszynski
Affiliation:
Department of Mathematics, Boise State University, Boise, Idaho 83725, USA, E-mail: [email protected], URL: http://math.boisestate.edu/~tomek
Saharon Shelah*
Affiliation:
Mathematics Department, Rutgers University, New Brunswick, NJ 08903, USA, E-mail: [email protected], URL: http://math.rutgers.edu/~shelah
Boaz Tsaban
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel, E-mail: [email protected], URL: http://www.cs.biu.ac.il/~tsaban
*
Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

We answer a question of Just, Miller, Scheepers and Szeptycki whether certain diagonalization properties for sequences of open covers are provably closed under taking finite or countable unions.

Keywords

Menger propertyHurewicz propertyselection principlesnear coherence of filters
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1254 - 1260
Copyright
Copyright © Association for Symbolic Logic 2003

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] Bartoszynski, I., Shelah, S., and Tsaban, B., Additivity properties of topological diagonalizations, (full version). Available at http://arxiv.org/abs/math.LO/0112262.Google Scholar
[2] Blass, A. R., Near coherence of filters I: Cofinal equivalence of models of arithmetic, Notre Dame Journal of Formal Logic, vol. 27 (1986), pp. 579–591.CrossRefGoogle Scholar
[3] Blass, A. R., Near coherence of filters III: A simplified consistency proof, Notre Dame Journal of Formal Logic, vol. 30 (1989), no. 4, pp. 530–538.CrossRefGoogle Scholar
[4] Blass, A. R., Nearly adequate sets. Logic and algebra (Zhang, Y., editor), Contemporary Mathematics, vol. 302, 2002, pp. 33–48.Google Scholar
[5] Galvin, F. and Miller, A. W., γ-sets and other singular sets of reals, Topology and its Applications, vol. 17 (1984), pp. 145–155.CrossRefGoogle Scholar
[6] Hurewicz, W., Über folgen stetiger funktionen. Fundamenta Mathematicae, vol. 9 (1927), pp. 193–204.CrossRefGoogle Scholar
[7] Just, W., Miller, A. W., Scheepers, M., and Szeptycki, P. J., The combinatorics of open covers II, Topology and its Applications, vol. 73 (1996), pp. 241–266.CrossRefGoogle Scholar
[8] Recław, I., Every Luzin set is undetermined in the point-open game, Fundamenta Mathematicae, vol. 144 (1994), pp. 43–54.CrossRefGoogle Scholar
[9] Scheepers, M., The length of some diagonalization games, Archive for Mathematical Logic, vol. 38 (1999), pp. 103–122.CrossRefGoogle Scholar
[10] Scheepers, M., Sequential convergence in Cp(X) and a covering property, East-West Journal of Mathematics, vol. 1 (1999), pp. 207–214.Google Scholar
[11] Scheepers, M. and Tsaban, B., The combinatorics of Borel covers, Topology and its Applications, vol. 121 (2002), pp. 357–382.CrossRefGoogle Scholar
[12] Tsaban, B., A diagonalization property between Hurewicz and Menger, Real Analysis Exchange, vol. 27 (2001/2002), pp. 757–763.CrossRefGoogle Scholar