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A stability transfer theorem in d -tame metric abstract elementary classes

Pedro Zambrano

Mathematical Logic Quarterly 58 (4-5):333-341 (2012)

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Categoricity from one successor cardinal in Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (2):181-201.details We prove that from categoricity in λ+ we can get categoricity in all cardinals ≥ λ+ in a χ-tame abstract elementary classe [Formula: see text] which has arbitrarily large models and satisfies the amalgamation and joint embedding properties, provided [Formula: see text] and λ ≥ χ. For the missing case when [Formula: see text], we prove that [Formula: see text] is totally categorical provided that [Formula: see text] is categorical in [Formula: see text] and [Formula: see text]. Download Export citation Bookmark 29 citations
Upward Stability Transfer for Tame Abstract Elementary Classes.John Baldwin, David Kueker & Monica VanDieren - 2006 - Notre Dame Journal of Formal Logic 47 (2):291-298.details Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We name some variants of tameness and prove the following. Let K be an AEC with Löwenheim-Skolem number ≤κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then K is Galois-stable in κ⁺ⁿ for all n<ω. With one further hypothesis we get a very strong conclusion in the countable case. Let K be an AEC satisfying the amalgamation property (...) Download Export citation Bookmark 19 citations
Uniqueness of limit models in classes with amalgamation.Rami Grossberg, Monica VanDieren & Andrés Villaveces - 2016 - Mathematical Logic Quarterly 62 (4-5):367-382.details 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. Download Export citation Bookmark 19 citations

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