Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T07:33:22.164Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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