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Media type:
E-Article
Title:
TAMENESS FROM LARGE CARDINAL AXIOMS
Contributor:
BONEY, WILL
Published:
Association for Symbolic Logic, Inc., 2014
Published in:
The Journal of Symbolic Logic, 79 (2014) 4, Seite 1092-1119
Language:
English
ISSN:
0022-4812;
1943-5886
Origination:
Footnote:
Description:
We show that Shelah's Eventual Categoricity Conjecture for successors follows from the existence of class many strongly compact cardinals. This is the first time the consistency of this conjecture has been proven. We do so by showing that every AEC with LS(K) below a strongly compact cardinal κ is < κ-tame and applying the categoricity transfer of Grossberg and VanDieren [11]. These techniques also apply to measurable and weakly compact cardinals and we prove similar tameness results under those hypotheses. We isolate a dual property to tameness, called type shortness, and show that it follows similarly from large cardinals.