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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
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.