40 citations · 107 across the 15 of their papers we have counts for
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Categoricity from one successor cardinal in Tame Abstract Elementary Classes
Rami Grossberg, Monica VanDieren
Let K be an abstract elementary classes which has arbitrarily large models and satisfies the amalgamation and joint embedding properties. Theorem 1. Suppose K is χ-tame. If K is ca…
Abstract decomposition theorem and applications
Rami Grossberg, Olivier Lessmann
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomp…
Galois-stability for Tame Abstract Elementary Classes
Rami Grossberg, Monica VanDieren
We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this…
Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes
Rami Grossberg, Monica VanDieren
Let K be an Abstract Elemenetary Class satisfying the amalgamation and the joint embedding property, let μbe the Hanf number of K. Suppose K is tame. MAIN COROLLARY: (ZFC) If K is…
Excellent Abstract Elementary Classes are tame
Rami Grossberg, Alexei S. Kolesnikov
The assumption that an AEC is tame is a powerful assumption permitting development of stability theory for AECs with the amalgamation property. Lately several upward categoricity t…
Uniqueness of Limit Models in Classes with Amalgamation
R. Grossberg, M. VanDieren, A. Villaveces
Let K be an abstract elementary class satisfying the joint embedding and the amalgamation properties. Let m be a cardinal above the the Löwenheim-Skolem number of the class. Suppos…