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Menger's covering property and groupwise density

Published online by Cambridge University Press:  12 March 2014

Boaz Tsaban  and
Lyubomyr Zdomskyy
Boaz Tsaban
Affiliation:
Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel.E-mail:boaz.tsaban@weizmann.ac.il, URL:http://www.cs.biu.ac.il/~tsaban
Lyubomyr Zdomskyy
Affiliation:
Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv 79000, Ukraine.E-mail:lzdomsky@rambler.ru
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Abstract

We establish a surprising connection between Menger's classical covering property and Blass-Laflamme's modern combinatorial notion of groupwise density. This connection implies a short proof of the groupwise density bound on the additivity number for Menger's property.

Keywords

Menger propertygroupwise density

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 3 , September 2006 , pp. 1053 - 1056
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

[1]Blass, A., Groupwise density and related cardinals, Archive for Mathematical Logic, vol. 30 (1990), pp. 1–11.CrossRefGoogle Scholar
[2]Blass, A., Combinatorial cardinal characteristics of the continuum, Handbook of set theory (Foreman, M., Kanamori, A., and Magidor, M., editors), Kluwer Academic Publishers, Dordrecht, to appear.Google Scholar
[3]Blass, A. and Laflamme, C., Consistency results about filters and the number of inequivalent growth types, this Journal, vol. 54 (1989), pp. 50–56.Google Scholar
[4]Blass, A. and Mildenberger, H., On the cofinality of ultrapowers, this Journal, vol. 64 (1999), pp. 727–736.Google Scholar
[5]Hurewicz, W., Über eine Verallgemeinerung des Borelschen Theorems, Mathematische Zeitschrift, vol. 24 (1925), pp. 401–421.CrossRefGoogle Scholar
[6]Hurewicz, W., Über Folgen stetiger Funktionen, Fundamenta Mathematicae, vol. 9 (1927), pp. 193–204.CrossRefGoogle Scholar
[7]Menger, K., Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberichte der Wiener Akademie, vol. 133 (1924), pp. 421–444.Google Scholar
[8]Recław, I., Every Luzin set is undetermined in point-open game, Fundamenta Mathematicae, vol. 144 (1994), pp. 43–54.CrossRefGoogle Scholar
[9]Scheepers, M., Selection principles and covering properties in topology, Note di Matematica, vol. 22 (2003), pp. 3–41.Google Scholar
[10]Tsaban, B., Additivity numbers of covering properties, Selection principles and covering properties in topology (Kočinac, L. D. R., editor), Quaderni di Matematica, to appear, http://arxiv.org/abs/math.GN/0604451.Google Scholar
[11]Tsaban, B., Some new directions in infinite-combinatorial topology, Set theory (Bagaria, J. and Todorčevic, S., editors), Trends in Mathematics, Birkhauser, to appear 2006, http://arxiv.org/abs/math.GN/0409069.Google Scholar
[12]Tsaban, B. and Zdomskyy, L., Scales, fields, and a problem of Hurewicz, http://arxiv.org/abs/math.GN/0507043, submitted.Google Scholar
[13]Zdomskyy, L., A semifilter approach to selection principles, Commentationes Mathematicae Universitatis Carolinae, vol. 46 (2005), pp. 525–540.Google Scholar