 

Jinglun Cai and
Konstantinos Tsaprounis
On strengthenings of superstrong cardinals
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Published: 
January 20, 2019. 
Keywords: 
Superstrong cardinals, extendible cardinals, C^{(n)}cardinals, Laver functions. 
Subject: 
03E35, 03E55. 


Abstract
We consider some natural strengthenings of the wellknown notion of superstrong cardinal, looking at their corresponding C^{(n)}versions as well, studying their properties and their connections with other usual large cardinals. In particular, we introduce the notions of
C^{(n)}ultrastrongness and of C^{(n)}global superstrongness. As it turns out, the former is closely related to
C^{(n)}extendibility, a rather robust large cardinal assumption that has found applications in other mathematical areas, while for the latter, among other things, we show that appropriate Laver functions exist, making it the second known example of a C^{(n)}hierarchy that has this feature. 

Acknowledgements
The authors are grateful to Joan Bagaria for many helpful conversations. Further gratitude goes to the anonymous referee for his/her valuable comments and suggestions.


Author information
Jinglun Cai:
University of Barcelona
Faculty of Mathematics and Computer Science
Gran Via de les Corts Catalanes 585
08007 Barcelona, Catalonia, Spain
jinglun.cn@gmail.com
Konstantinos Tsaprounis:
Department of Mathematics
University of the Aegean
Samos, Greece
kostas.tsap@gmail.com

