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Elementary embeddings and infinitary combinatorics

Published online by Cambridge University Press:  12 March 2014

Kenneth Kunen*
Affiliation:
University of Wisconsin, Madison, Wisconsin

Extract

One of the standard ways of postulating large cardinal axioms is to consider elementary embeddings, j, from the universe, V, into some transitive submodel, M. See Reinhardt–Solovay [7] for more details. If j is not the identity, and κ is the first ordinal moved by j, then κ is a measurable cardinal. Conversely, Scott [8] showed that whenever κ is measurable, there is such j and M. If we had assumed, in addition, that , then κ would be the κth measurable cardinal; in general, the wider we assume M to be, the larger κ must be.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1972

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References

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