Rank Functions and Partial Stability Spectra for Tame Abstract Elementary Classes

Notre Dame Journal of Formal Logic 54 (2):153-166 (2013)
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Abstract

We introduce a family of rank functions and related notions of total transcendence for Galois types in abstract elementary classes. We focus, in particular, on abstract elementary classes satisfying the condition known as tameness, where the connections between stability and total transcendence are most evident. As a byproduct, we obtain a partial upward stability transfer result for tame abstract elementary classes stable in a cardinal $\lambda$ satisfying $\lambda^{\aleph_{0}}\gt \lambda$, a substantial generalization of a result of Baldwin, Kueker, and VanDieren

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Citations of this work

Tameness and extending frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.
Forking in short and tame abstract elementary classes.Will Boney & Rami Grossberg - 2017 - Annals of Pure and Applied Logic 168 (8):1517-1551.
Tameness and frames revisited.Will Boney & Sebastien Vasey - 2017 - Journal of Symbolic Logic 82 (3):995-1021.

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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.
Examples of non-locality.John T. Baldwin & Saharon Shelah - 2008 - Journal of Symbolic Logic 73 (3):765-782.

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