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TAMENESS FROM LARGE CARDINAL AXIOMS

Published online by Cambridge University Press:  12 December 2014

WILL BONEY
WILL BONEY*
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES CARNEGIE MELLON UNIVERSITY PITTSBURGH, PENNSYLVANIA, USAE-mail: wboney@cmu.edu
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Abstract

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.

Keywords

Abstract Elementary Classestamenesslarge cardinals
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 4 , December 2014 , pp. 1092 - 1119
Copyright
Copyright © The Association for Symbolic Logic 2014 

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