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
Ramsey-Like Cardinals II.Victoria Gitman & P. D. Welch - 2011 - Journal of Symbolic Logic 76 (2):541-560.
View all 9 references / Add more references
Citations of this work BETA
Virtual Large Cardinals.Victoria Gitman & Ralf Schindler - 2018 - Annals of Pure and Applied Logic 169 (12):1317-1334.
What is the Theory ZFC Without Power Set?Victoria Gitman, Joel David Hamkins & Thomas A. Johnstone - 2016 - Mathematical Logic Quarterly 62 (4-5):391-406.
Greatly Erdős Cardinals with Some Generalizations to the Chang and Ramsey Properties.I. Sharpe & P. D. Welch - 2011 - Annals of Pure and Applied Logic 162 (11):863-902.
Inner Models with Large Cardinal Features Usually Obtained by Forcing.Arthur W. Apter, Victoria Gitman & Joel David Hamkins - 2012 - Archive for Mathematical Logic 51 (3-4):257-283.
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.
View all 12 citations / Add more citations
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