904. Will Boney and Sebastien Vasey Categoricity and infinitary logics
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Submission date: 13 August 2015.
Abstract:
We use model-theoretic forcing to show:
Theorem
Let K be an abstract elementary class categorical in
unboundedly many cardinals. Then there exists a cardinal λ such that
whenever M, N in K have size at least λ, M ≤ N if and only if M
\preceq_{L_{∞, LS(K)^+}} N. This fixes a gap in Shelah's proof of
the following result:
Theorem
Let K be an abstract elementary class categorical in unboundedly many
cardinals. Then the class of λ such that:
1) K is categorical in λ;
2) K has amalgamation in λ; and
3) there is a good λ-frame with underlying class K_λ is
stationary.