Uniqueness of limit models in classes with amalgamation |
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| Authors: | Rami Grossberg Monica VanDieren Andrés Villaveces |
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| Institution: | 1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, United States of America;2. Department of Mathematics & University Honors Program, Robert Morris University, Moon Township, PA, United States of America;3. Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia |
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| Abstract: | We prove the following main theorem: Let  be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality μ. Let μ be a cardinal above the the Löwenheim‐Skolem number of the class. If  is μ‐Galois‐stable, has no μ‐Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two  ‐limits over M, for  , are isomorphic over M. |
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