Shelah's stability spectrum and homogeneity spectrum in finite diagrams

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Archive for Mathematical Logic 41 (1):1-31 (2002)
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Abstract

We present Saharon Shelah's Stability Spectrum and Homogeneity Spectrum theorems, as well as the equivalence between the order property and instability in the framework of Finite Diagrams. Finite Diagrams is a context which generalizes the first order case. Localized versions of these theorems are presented. Our presentation is based on several papers; the point of view is contemporary and some of the proofs are new. The treatment of local stability in Finite Diagrams is new.

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10.1007/s001530200000

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Citations of this work

Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
Toward a stability theory of tame abstract elementary classes.Sebastien Vasey - 2018 - Journal of Mathematical Logic 18 (2):1850009.
Forking in short and tame abstract elementary classes.Will Boney & Rami Grossberg - 2017 - Annals of Pure and Applied Logic 168 (8):1517-1551.

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References found in this work

Model theory for infinitary logic.H. Jerome Keisler - 1971 - Amsterdam,: North-Holland Pub. Co..
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.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.

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