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Cardinal characteristics on graphs

Published online by Cambridge University Press:  12 March 2014

Nick Haverkamp
Nick Haverkamp*
Affiliation:
Humboldt Universität, Institut für Philosophie, Unter den Linden 6, 10099 Berlin, Germany, E-mail: Nick_Haverkamp@web.de
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Abstract

A cardinal characteristic can often be described as the smallest size of a family of sequences which has a given property. Instead of this traditional concern for a smallest realization of the given property, a basically new approach, taken in [4] and [5], asks for a realization whose members are sequences of labels that correspond to 1-way infinite paths in a labelled graph. We study this approach as such, establishing tools that are applicable to all these cardinal characteristics. As an application, we demonstrate the power of the tools developed by presenting a short proof of the bounded graph conjecture [4].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 1 - 33
Copyright
Copyright © Association for Symbolic Logic 2011

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References

REFERENCES

[1]Blass, A., Combinatorial cardinal characteristics of the continuum, Handbook of set theory (Foreman, M. and Kanamori, A., editors), Springer, 2010, pp. 395–490.CrossRefGoogle Scholar
[2]Diestel, R., The classification offinitely spreading graphs, Proceedings of the London Mathematical Society, vol. 73 (1996), no. 3, pp. 534–554.CrossRefGoogle Scholar
[3]Diestel, R., Graph theory, 3rd ed., Springer, Heidelberg, 2005.Google Scholar
[4]Diestel, R. and Leader, I.B., A proof of the bounded graph conjecture, Inventiones mathematicae, vol. 108 (1992), pp. 131–162.CrossRefGoogle Scholar
[5]Diestel, R., Shelah, S., and Steprans, J., Dominating functions and graphs, Journal of the London Mathematical Society, vol. 49 (1994), pp. 16–24.CrossRefGoogle Scholar
[6]Halin, R., Über die Maximalzahl fremder unendlicher Wege, Mathematische Nachrichten, vol. 30 (1965), pp. 63–85.CrossRefGoogle Scholar