Elementary embeddings and infinitary combinatorics
- 1 September 1971
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 36 (3) , 407-413
- https://doi.org/10.2307/2269948
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.Keywords
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