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A set mapping with no infinite free subsets

Published online by Cambridge University Press:  12 March 2014

P. Komjáth
P. Komjáth*
Affiliation:
Department of Computer Science, Loránd Eötvös University, 1088 Budapest, Hungary
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Abstract

It is consistent that there exists a set mapping F: [ω2]2 → [ω2]<ω such that F(α,β) ⊆ α for α < β < ω2 and there is no infinite free subset for F. This solves a problem of A. Hajnal and A. Máté.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1400 - 1402
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

[1]Baumgartner, J. E. and Shelah, S., Remarks on superatomic Boolean algebras, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 109–129.CrossRefGoogle Scholar
[2]Erdős, P. and Hajnal, A., On the structure of mappings, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 9 (1958), pp. 111–131.CrossRefGoogle Scholar
[3]Hajnal, A. and Máté, A., Set mappings, partitions, and chromatic numbers, Logic Colloquium 73, North-Holland, Amsterdam, 1975, pp. 347–379.Google Scholar
[4]Shelah, S. and Stanley, L., A theorem and some consistency results in partition calculus, Annals of Pure and Applied Logic, vol. 36 (1987), pp. 119–152.CrossRefGoogle Scholar