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A note on cardinal exponentiation

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Affiliation:
Hebrew University, Jerusalem, Israel University of California, Berkeley, CA 94720

Abstract

Silver and subsequently Galvin and Hajnal, got bounds on , for ℵα strong limit cardinal of cofinality > ℵ0. We somewhat improve those results.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1980

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References

REFERENCES

[DJ]Devlin, K. and Jensen, R.B., Marginalia to a theorem of Silver (to appear).Google Scholar
[BP]Baumgartner, J. E. and Prikry, K., On the theorem of Silver, Discrete Mathematics, 14(1976), pp. 1722.CrossRefGoogle Scholar
[G]Gaifman, H., Operations on rational structures, functions and classes. I, Procedings of the Tarski Symposium, Proceedings of Symposia in Pure Mathematics, Berkeley, 1971, vol. XXV, American Mathematical Society, 1974, pp. 2140.Google Scholar
[GH]Galvin, F. and Hajnal, A., Inequalities for cardinal powers, Annals of Mathematics, vol. 101(1975), pp. 491498.CrossRefGoogle Scholar
[JP]Jech, T. and Prikry, K., On ideals of sets and the power set operation (preprint).Google Scholar
[Mg 1]Magidor, M., Chang conjecture and powers of singular cardinals, this Journal, vol. 42 (1977), pp. 272276.Google Scholar
[Mg 2]Magidor, M., On the singular cardinal problem. I, Israel Journal of Mathematics, vol. 28 (1977), pp. 131.CrossRefGoogle Scholar
[Mg 3]Magidor, M., On the singular cardinal problem. II, Annals of Mathematics, vol. 106 (1977), pp.517547.CrossRefGoogle Scholar
[S]Silver, J., On the singular cardinal problem, Proceedings of the International Congress of Mathematicians, Vancouver, 1974, vol. I, pp. 265268.Google Scholar
[Sh 1]Shelah, S., On powers of singular cardinals, compactness of second order logic, Notices of the American Mathematical Society, vol. 23(1976), p. A449.Google Scholar
[Sh 2]Shelah, S., Jonsson algebras in successor cardinality, Israel Journal of Mathematics, vol 30(1978), pp. 5764.CrossRefGoogle Scholar
[Sh 2]Shelah, S., Jonson algebras in successor cardinality, Israel Journal of Mathematics (to appear).Google Scholar
[Sh 3]Shelah, S., remarks to the book on partition calculus of Erdös, Hajnal, Mate and Rado, mimeograph, winter 19751976.Google Scholar