Ramsey-like cardinals

Publisher： Cambridge University Press

E-ISSN： 1943-5886|76|2|519-540

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.76, Iss.2, 2011-06, pp. : 519-540

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Abstract

One of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. We introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. These new axioms serve to further our knowledge about the elementary embedding properties of smaller large cardinals, in particular those still consistent with V = L.

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