Uniqueness of Limit Models in Classes with Amalgamation

Details Uniqueness of Limit Models in Classes with Amalgamation Uniqueness of Limit Models in Classes with Amalgamation

2005-09-15

arxiv.org/abs/math/0509338v2

Mathematics

Logic

20 pages, 1 figure

Scientific paper

We prove: [Main Theorem] Let K be an AEC and m > LS(K). Suppose K satisfies the disjoint amalgamation property for models of cardinality m. If K is m-Galois-stable, does not have long splitting chains, and satisfies locality of splitting, then any two (m,s_l)$-limits over a model M (for l in {1,2}) are isomorphic over M. This result extends results of Shelah from [Sh 394], [Sh 576], [Sh 600], Kolman and Shelah in [KoSh] and Shelah and Villaveces from [ShVi]. Our uniqueness theorem was used by Grossberg and VanDieren to prove a case of Shelah's categoricity conjecture for tame AEC in [GrVa 2].

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