Abstract
AbstractWe 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 withLS(K) below a strongly compact cardinalκis <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, calledtype shortness, and show that it follows similarly from large cardinals.
Publisher
Cambridge University Press (CUP)
Reference38 articles.
1. Categoricity of theories inLκω, when κ is a measureable cardinal, part 1;Kolman;Fundamenta Mathematica,1996
2. GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES
3. [32] Shelah Saharon , Categoricity in Abstract Elementary Classes: Going up inductively , math.LO/0011215.
4. Almost Free Modules
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