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Independence of strong partition relation for small cardinals, and the free-subset problem

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Saharon Shelah*
Affiliation:
Hebrew University of Jerusalem, Jerusalem, Israel
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Abstract

We prove the independence of a strong partition relation on ℵω, answering a question of Erdös and Hajnal. We then give an almost complete answer to the free subset problem.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 45 , Issue 3 , September 1980 , pp. 505 - 509
Copyright
Copyright © Association for Symbolic Logic 1980

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References

REFERENCES

[Eh 1]Erdös, P. and Hajnal, A., Unsolved problems in set theory, U.C.L.A. Symposium, 1967; (Scott, , Editor), Proceedings of Symposia in Pure Mathematics, Vol. XII, Part I, American Mathematical Society, Providence, R.I., 1971, pp. 17–48.Google Scholar
[EH 2]Erdös, P. and Hajnal, A., Unsolved and solved problems in set theory, Tarski 70th Birthday Symposium, Berkeley, 1971 (Henkin, , Editor), Proceedings of Symposia in Pure Mathematics, Vol. XXV, American Mathematical Society, Providence, R.I., 1974, pp. 269–288.Google Scholar
[EH 3]Erdös, P. and Hajnal, A., On a problem of B. Jonsson, Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 14 (1966), pp. 19–23.Google Scholar
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