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Supercompact cardinals, elementary embeddings and fixed points1
Published online by Cambridge University Press: 12 March 2014
Extract
Supercompactness is usually defined in terms of the existence of certain ultrafilters. By the well-known procedure of taking ultrapowers of V (the universe of sets) and transitive collapses, one obtains transitive inner models of V and corresponding elementary embeddings from V into these inner models. These embeddings have been studied extensively (see, e.g. [3] or [4]). We investigate the action of these embeddings on cardinals. In particular, we establish a characterization, based upon cofinality, of which cardinals are fixed by these embeddings.
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- Research Article
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- Copyright © Association for Symbolic Logic 1982
Footnotes
1
This paper is part of the author's Ph.D. thesis [1] written at the State University of New York at Buffalo under the supervision of Professor Nicolas Goodman to whom the author is grateful.
References
REFERENCES
[1]Barbanel, J. B., Results on supercompact cardinals, Ph.D. Thesis, State University of New York at Buffalo, 1979.Google Scholar
[3]Solovay, R. M.Strongly compact cardinals and the G.C. H., Proceedings of the Tarski Symosium (Henkin, L.et al., Editors), Proceedings of Symposia in Pure Mathematics, vol. 25, American Mathematical Society, Providence, R.I., 1974, pp. 365–372.CrossRefGoogle Scholar
[4]Solovay, R. M., Reinhardt, W. N. and Kanamori, A., Strong axioms of infinity and elementary embeddings, Annals of Mathematical Logic, vol. 13, No. 1 (1978), pp. 73–116.CrossRefGoogle Scholar