Elementary embeddings and infinitary combinatorics

Journal of Symbolic Logic 36 (3):407-413 (1971)
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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.

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Citations of this work

Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
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References found in this work

General Topology.John L. Kelley - 1962 - Journal of Symbolic Logic 27 (2):235-235.
Some applications of iterated ultrapowers in set theory.Kenneth Kunen - 1970 - Annals of Mathematical Logic 1 (2):179.

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