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The consistency of one fixed omega

Published online by Cambridge University Press:  12 March 2014

J. M. Henle
J. M. Henle*
Affiliation:
Department of Mathematics, Smith College, Northampton, Massachusetts 01063, E-mail: jhenle@smith.edu
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Abstract

The paper “Partitions of Products” [DiPH] investigated the polarized partition relation

The relation is consistent relative to an inaccessible cardinal if every αi is finite, but inconsistent if two are infinite. We show here that it consistent (relative to an inaccessible) for one to be infinite.

Along the way, we prove an interesting proposition from ZFC concerning partitions of the finite subsets of ω.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 1 , March 1995 , pp. 172 - 177
Copyright
Copyright © Association for Symbolic Logic 1995

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References

REFERENCES

[CDiP]Carnielli, W. A. and Di Prisco, C. A., Some results on polarized partition relations of higher dimension, Quarterly of Mathematical Logic, vol. 39, 1993, pp. 461–474.CrossRefGoogle Scholar
[DiPH]Di Prisco, C. A. and Henle, J. M., Partitions of products, this Journal, vol. 58 (1993), pp. 860–871.Google Scholar
[GP]Galvin, F. and Priky, K., Borel sets and Ramsey's theorem, this Journal, vol. 38 (1973), pp. 193–198.Google Scholar
[M]Mathias, A. R. D., Happy families, Annals of Mathematical Logic, vol. 12, 1977, pp. 59–111.CrossRefGoogle Scholar