Journal of Symbolic Logic 76 (2):519 - 540 (2011)

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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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DOI 10.2178/jsl/1305810762
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References found in this work BETA

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Ramsey-Like Cardinals II.Victoria Gitman & P. D. Welch - 2011 - Journal of Symbolic Logic 76 (2):541-560.
Ramsey Cardinals and Constructibility.William Mitchell - 1979 - Journal of Symbolic Logic 44 (2):260-266.
Some Applications of Iterated Ultrapowers in Set Theory.Kenneth Kunen - 1970 - Annals of Mathematical Logic 1 (2):179.
A Hierarchy of Ramsey Cardinals.Qi Feng - 1990 - Annals of Pure and Applied Logic 49 (3):257-277.

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Citations of this work BETA

Virtual Large Cardinals.Victoria Gitman & Ralf Schindler - 2018 - Annals of Pure and Applied Logic 169 (12):1317-1334.
Large Cardinals Need Not Be Large in HOD.Yong Cheng, Sy-David Friedman & Joel David Hamkins - 2015 - Annals of Pure and Applied Logic 166 (11):1186-1198.

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