Ramsey-like cardinals

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

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 89,654

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Abstract logic and set theory. II. large cardinals.Jouko Väänänen - 1982 - Journal of Symbolic Logic 47 (2):335-346.
On elementary embeddings from an inner model to the universe.J. Vickers & P. D. Welch - 2001 - Journal of Symbolic Logic 66 (3):1090-1116.
Chains of end elementary extensions of models of set theory.Andrés Villaveces - 1998 - Journal of Symbolic Logic 63 (3):1116-1136.
On measurable limits of compact cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
Strongly unfoldable cardinals made indestructible.Thomas A. Johnstone - 2008 - Journal of Symbolic Logic 73 (4):1215-1248.
Proper forcing and remarkable cardinals II.Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (3):1481-1492.
Laver sequences for extendible and super-almost-huge cardinals.Paul Corazza - 1999 - Journal of Symbolic Logic 64 (3):963-983.
Large cardinals and large dilators.Andy Lewis - 1998 - Journal of Symbolic Logic 63 (4):1496-1510.

Analytics

Added to PP
2013-09-30

Downloads
22 (#599,714)

6 months
3 (#433,579)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

What is the theory without power set?Victoria Gitman, Joel David Hamkins & Thomas A. Johnstone - 2016 - Mathematical Logic Quarterly 62 (4-5):391-406.
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.
Small models, large cardinals, and induced ideals.Peter Holy & Philipp Lücke - 2021 - Annals of Pure and Applied Logic 172 (2):102889.

View all 14 citations / Add more citations

References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
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