Tameness and extending frames

Journal of Mathematical Logic 14 (2):1450007 (2014)
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Abstract

We combine two notions in AECs, tameness and good λ-frames, and show that they together give a very well-behaved nonforking notion in all cardinalities. This helps to fill a longstanding gap in classification theory of tame AECs and increases the applicability of frames. Along the way, we prove a complete stability transfer theorem and uniqueness of limit models in these AECs.

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10.1142/s021906131450007x

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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.
Building independence relations in abstract elementary classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.
Canonical forking in AECs.Will Boney, Rami Grossberg, Alexei Kolesnikov & Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (7):590-613.
Toward a stability theory of tame abstract elementary classes.Sebastien Vasey - 2018 - Journal of Mathematical Logic 18 (2):1850009.

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References found in this work

Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
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.
Non-forking frames in abstract elementary classes.Adi Jarden & Saharon Shelah - 2013 - Annals of Pure and Applied Logic 164 (3):135-191.

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