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Elementary embeddings and infinitary combinatorics

Published online by Cambridge University Press:  12 March 2014

Kenneth Kunen
Kenneth Kunen*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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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
Information
The Journal of Symbolic Logic , Volume 36 , Issue 3 , September 1971 , pp. 407 - 413
Copyright
Copyright © Association for Symbolic Logic 1972

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References

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