Categoricity from one successor cardinal in Tame abstract elementary classes

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Journal of Mathematical Logic 6 (2):181-201 (2006)
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Abstract

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].

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10.1142/s0219061306000554

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Citations of this work

Shelah's eventual categoricity conjecture in universal classes: Part I.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (9):1609-1642.
Forking and superstability in Tame aecs.Sebastien Vasey - 2016 - Journal of Symbolic Logic 81 (1):357-383.
Canonical forking in AECs.Will Boney, Rami Grossberg, Alexei Kolesnikov & Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (7):590-613.
Building independence relations in abstract elementary classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.

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References found in this work

Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
Toward categoricity for classes with no maximal models.Saharon Shelah & Andrés Villaveces - 1999 - Annals of Pure and Applied Logic 97 (1-3):1-25.
Categoricity in abstract elementary classes with no maximal models.Monica VanDieren - 2006 - Annals of Pure and Applied Logic 141 (1):108-147.

View all 8 references / Add more references