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math.LO2005★ 1 cited
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…
math.LO2005★ 1 cited
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…
math.LO2004
Succinct Definitions in the First Order Theory of Graphs
Oleg Pikhurko, Joel Spencer, Oleg Verbitsky
We say that a first order sentence A defines a graph G if A is true on G but false on any graph non-isomorphic to G. Let L(G) (resp. D(G)) denote the minimum length (resp. quantifi…