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Canonical Partition Relations

Published online by Cambridge University Press:  12 March 2014

James E. Baumgartner
James E. Baumgartner*
Affiliation:
Dartmouth College, Hanover, New Hampshire 03755
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Abstract

Several canonical partition theorems are obtained, including a simultaneous generalization of Neumer's lemma and the Erdös-Rado theorem. The canonical partition relation for infinite cardinals is completely determined, answering a question of Erdös and Rado. Counterexamples are given showing that in several ways these results cannot be improved.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 40 , Issue 4 , December 1975 , pp. 541 - 554
Copyright
Copyright © Association for Symbolic Logic 1975

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References

REFERENCES

[1] Baumgartner, J., Ineffability properties of cardinals. I, Proceedings of the International Colloquium on Infinite and Finite Sets (Keszthely, Hungary, 1973), pp. 109–130.Google Scholar
[2] Baumgartner, J. and Hajnal, A., A proof {involving Martin's axiom) of a partition relation, Fundamenta Mathematicae, vol. 78 (1973), pp. 193–203.CrossRefGoogle Scholar
[3] Erdös, P., Hajnal, A. and Rado, R., Partition relations for cardinal numbers, Acta Mathematica (Hung.), vol. 16 (1965), pp. 93–196.Google Scholar
[4] Erdos, P. and Rado, R., A combinatorial theorem, Journal of the London Mathematical Society, vol. 25 (1950), pp. 249–255.Google Scholar
[5] Erdos, P. and Rado, R., Combinatorial theorems on classifications of subsets of a given set, Proceedings of the London Mathematical Society (3), vol. 2 (1952), pp. 417–439.CrossRefGoogle Scholar
[6] Erdos, P. and Rado, R., A partition calculus in set theory, Bulletin of the American Mathematical Society, vol. 62 (1956), pp. 427–489.CrossRefGoogle Scholar
[7] Fodor, G., Eine Bemerkung zur Theorie der regressiven Funktionen, Acta Scientarium Mathematicum, vol. 17 (1956), pp. 139–142.Google Scholar
[8] Hajnal, A., Remarks on a theorem of W. P. Hanf, Fundamenta Mathematicae, vol. 54 (1964), pp. 109–113.Google Scholar
[9] Jensen, R. and Kunen, K., Some combinatorial properties of L and V (mimeographed).Google Scholar
[10] Neumer, W., Verallgemeinerung eines Satzes von Alexandroff und Urysohn, Mathematische Zeltschrift, vol. 54 (1951), pp. 254–261.Google Scholar
[11] Ramsey, F. P., On a problem of formal logic, Proceedings of the London Mathematical Society (2), vol. 30 (1930), pp. 264–286.Google Scholar
[12] Silver, J., Some applications of model theory in set theory, Annals of Mathematical Logic, vol. 3 (1971), pp. 45–110.CrossRefGoogle Scholar
[13] Simpson, S., Model-theoretic proof of a partition theorem, Notices of the American Mathematical Society, vol. 17 (1970), p. 964.Google Scholar