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Generic graph construction

Published online by Cambridge University Press:  12 March 2014

James E. Baumgartner
James E. Baumgartner*
Affiliation:
Dartmouth College, Hanover, New Hampshire 03755
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Abstract

It is shown that if ZF is consistent, then so is ZFC + GCH + “There is a graph with cardinality ℵ2 and chromatic number ℵ2 such that every subgraph of cardinality ≤ ℵ1, has chromatic number ≤ ℵ0”. This partially answers a question of Erdös and Hajnal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 1 , March 1984 , pp. 234 - 240
Copyright
Copyright © Association for Symbolic Logic 1984

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References

REFERENCES

[1]Erdös, P., Problems and results on finite and infinite combinatorial analysis, Infinite and finite sets (Hajnal, A., Rado, R. and Sós, V. T., editors), vol. I, Colloquia Mathematica Societatis János Bolyai, vol. 10, North-Holland, Amsterdam, 1975, pp. 403–424.Google Scholar
[2]Williams, N. H., Combinatorial set theory, North-Holland, Amsterdam, 1977.Google Scholar