Hostname: page-component-797576ffbb-pxgks Total loading time: 0 Render date: 2023-12-02T00:26:39.582Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

A note on cardinal exponentiation

Published online by Cambridge University Press:  12 March 2014

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


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

Research Article
Copyright © Association for Symbolic Logic 1980

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.)



[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.Google 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.Google 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.Google Scholar
[Mg 3]Magidor, M., On the singular cardinal problem. II, Annals of Mathematics, vol. 106 (1977), pp.517547.Google 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.Google 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