Abstract
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. Ifjis not the identity, andκis the first ordinal moved byj, thenκis a measurable cardinal. Conversely, Scott [8] showed that wheneverκis measurable, there is suchjandM. If we had assumed, in addition, that, thenκwould be theκth measurable cardinal; in general, the wider we assumeMto be, the largerκmust be.
Publisher
Cambridge University Press (CUP)
Reference8 articles.
1. Measurable cardinals and constructible sets;Scott;Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques,1961
2. On the GCH at measurable cardinals;Kunen;Proceedings of 1969 Logic Summer School at Manchester
3. Reinhardt W. and Solovay R. , Strong axioms of infinity and elementary embeddings, to appear.
4. Some applications of iterated ultrapowers in set theory
5. On a problem of B. Jónsson, Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques;Erdös;Astronomiques et Physiques,1966
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