Elementary chains and C (n)-cardinals

Archive for Mathematical Logic 53 (1-2):89-118 (2014)

Abstract
The C (n)-cardinals were introduced recently by Bagaria and are strong forms of the usual large cardinals. For a wide range of large cardinal notions, Bagaria has shown that the consistency of the corresponding C (n)-versions follows from the existence of rank-into-rank elementary embeddings. In this article, we further study the C (n)-hierarchies of tall, strong, superstrong, supercompact, and extendible cardinals, giving some improved consistency bounds while, at the same time, addressing questions which had been left open. In addition, we consider two cases which were not dealt with by Bagaria; namely, C (n)-Woodin and C (n)-strongly compact cardinals, for which we provide characterizations in terms of their ordinary counterparts. Finally, we give a brief account on the interaction of C (n)-cardinals with the forcing machinery
Keywords C (n)-cardinals  Woodin cardinals  Strongly compact cardinals
Categories (categorize this paper)
DOI 10.1007/s00153-013-0357-4
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 41,650
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
C (N)-Cardinals.Joan Bagaria - 2012 - Archive for Mathematical Logic 51 (3-4):213-240.
Tall Cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.
On Extendible Cardinals and the GCH.Konstantinos Tsaprounis - 2013 - Archive for Mathematical Logic 52 (5-6):593-602.
Canonical Seeds and Prikry Trees.Joel David Hamkins - 1997 - Journal of Symbolic Logic 62 (2):373-396.

Add more references

Citations of this work BETA

On Resurrection Axioms.Konstantinos Tsaprounis - 2015 - Journal of Symbolic Logic 80 (2):587-608.
Ultrahuge cardinals.Konstantinos Tsaprounis - 2016 - Mathematical Logic Quarterly 62 (1-2):77-87.
On Extensions of Supercompactness.Robert S. Lubarsky & Norman Lewis Perlmutter - 2015 - Mathematical Logic Quarterly 61 (3):217-223.
On C-Extendible Cardinals.Konstantinos Tsaprounis - 2018 - Journal of Symbolic Logic 83 (3):1112-1131.

Add more citations

Similar books and articles

Gap Forcing: Generalizing the Lévy-Solovay Theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
C (N)-Cardinals.Joan Bagaria - 2012 - Archive for Mathematical Logic 51 (3-4):213-240.
On the Indestructibility Aspects of Identity Crisis.Grigor Sargsyan - 2009 - Archive for Mathematical Logic 48 (6):493-513.
On Measurable Limits of Compact Cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
On Colimits and Elementary Embeddings.Joan Bagaria & Andrew Brooke-Taylor - 2013 - Journal of Symbolic Logic 78 (2):562-578.
On Extendible Cardinals and the GCH.Konstantinos Tsaprounis - 2013 - Archive for Mathematical Logic 52 (5-6):593-602.
Ramsey-Like Cardinals.Victoria Gitman - 2011 - Journal of Symbolic Logic 76 (2):519 - 540.
Chains of End Elementary Extensions of Models of Set Theory.Andrés Villaveces - 1998 - Journal of Symbolic Logic 63 (3):1116-1136.
Easton’s Theorem in the Presence of Woodin Cardinals.Brent Cody - 2013 - Archive for Mathematical Logic 52 (5-6):569-591.
Tall Cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.
Strongly Unfoldable Cardinals Made Indestructible.Thomas A. Johnstone - 2008 - Journal of Symbolic Logic 73 (4):1215-1248.

Analytics

Added to PP index
2013-11-23

Total views
43 ( #186,056 of 2,250,041 )

Recent downloads (6 months)
9 ( #155,493 of 2,250,041 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature