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A partially non-proper ordinal beyond L

Vincenzo Dimonte

Annals of Pure and Applied Logic 163 (9):1309-1321 (2012)

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(1 other version)Elementary embeddings and infinitary combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.details 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. Download Export citation Bookmark 59 citations
Coding lemmata in L.George Kafkoulis - 2004 - Archive for Mathematical Logic 43 (2):193-213.details Under the assumption that there exists an elementary embedding (henceforth abbreviated as and in particular under we prove a Coding Lemma for and find certain versions of it which are equivalent to strong regularity of cardinals below . We also prove that a stronger version of the Coding Lemma holds for a stationary set of ordinals below. Download Export citation Bookmark 7 citations
Reflection of elementary embedding axioms on the L[Vλ+1] hierarchy.Richard Laver - 2001 - Annals of Pure and Applied Logic 107 (1-3):227-238.details Say that the property Φ of a cardinal λ strongly implies the property Ψ. If and only if for every λ,Φ implies that Ψ and that for some λ′<λ,Ψ. Frequently in the hierarchy of large cardinal axioms, stronger axioms strongly imply weaker ones. Some strong implications are proved between axioms of the form “there is an elementary embedding j:Lα[Vλ+1]→Lα[Vλ+1] with ”. Download Export citation Bookmark 8 citations

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