Model Theoretic Characterizations of Large Cardinals Revisited
Will Boney, Stamatis Dimopoulos, Victoria Gitman, Menachem Magidor
TL;DR
This paper extends model theoretic characterizations to a broader class of large cardinals, including Woodin, virtual, and subtle cardinals, advancing the understanding of their foundational properties.
Contribution
It provides new model theoretic characterizations for Woodin, virtual, and subtle large cardinals, building on previous work on established large cardinal notions.
Findings
Characterizations for Woodin cardinals established
Virtual large cardinal characterizations developed
Subtle cardinal characterizations provided
Abstract
In [Bon20], model theoretic characterizations of several established large cardinal notions were given. We continue this work, by establishing such characterizations for Woodin cardinals (and variants), various virtual large cardinals, and subtle cardinals.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras