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Medientyp:
E-Artikel
Titel:
TAMENESS FROM LARGE CARDINAL AXIOMS
Beteiligte:
BONEY, WILL
Erschienen:
Association for Symbolic Logic, Inc., 2014
Erschienen in:The Journal of Symbolic Logic
Sprache:
Englisch
ISSN:
1943-5886;
0022-4812
Entstehung:
Anmerkungen:
Beschreibung:
<p>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.</p>