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Canonization theorems and applications

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Affiliation:
The Hebrew University, Jerusalem, Israel

Abstract

We improve the canonization theorems generalizing the Erdös-Rado theorem, and as a result complete the answer to “When does a Hausdorff space of cardinality χ necessarily have a discrete subspace of cardinality k” We also improve the results on existence of free subsets.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1981

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References

[EHR]Erdös, P., Hajnal, A. and Rado, R., Partition relations for cardinal numbers, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16 (1965), pp. 93196.CrossRefGoogle Scholar
[EHMR]Erdös, P., Hajnal, A., Mate, A. and Rado, R., Partition calculus, manuscript of a book, fall 1975.Google Scholar
[H]Hajnal, A., Proof of a conjecture of S. Ruziewicz, Fundamenta Mathematicae, vol. 50 (1961), pp. 123128.CrossRefGoogle Scholar
[J]Juhasz, I., Cardinal functions in topology, North-Holland, Amsterdam, 1971.Google Scholar
[Sh 1]Shelah, S., Notes in partition calculus, Infinite and finite sets, Proceedings of a Symposium in Honor of P. Erdös, 60th birthday, held in Hungary, 1973, Colloquium Mathematica Societatis Janos Bolaye 10 (Hajnal, Rado and Sos, Editors), North-Holland, Amsterdam, Vol. Ill, 1975, pp. 1115–1126.Google Scholar
[Sh 2]Shelah, S., Remark to the book on partition calculus, mimeograph, 01 1975.Google Scholar
[Sh 3]Shelah, S., Independence of strong partition relation for small cardinals, and the free subset problem, this Journal, vol. 45 (1980), pp. 505509.Google Scholar
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