14 citations · 17 across the 5 of their papers we have counts for
5 papers
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…