Elementary chains and C (n)-cardinals

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

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Citations of this work

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References found in this work

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.

View all 8 references / Add more references