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A rank for the class of elementary submodels of a superstable homogeneous model

Tapani Hyttinen & Olivier Lessmann

Journal of Symbolic Logic 67 (4):1469-1482 (2002)

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Shelah's stability spectrum and homogeneity spectrum in finite diagrams.Rami Grossberg & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (1):1-31.details 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. Download Export citation Bookmark 18 citations
Finite diagrams stable in power.Saharon Shelah - 1970 - Annals of Mathematical Logic 2 (1):69-118.details Download Export citation Bookmark 57 citations
Ranks and pregeometries in finite diagrams.Olivier Lessmann - 2000 - Annals of Pure and Applied Logic 106 (1-3):49-83.details The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D. In this work, we introduce a natural dependence relation on the subsets of the models for the 0-stable case which share many of the formal properties of forking. This (...) Download Export citation Bookmark 14 citations
Strong splitting in stable homogeneous models.Tapani Hyttinen & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):201-228.details In this paper we study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in Hyttinen 167–182). We apply this to prove a structure theorem. We also show that dop and sdop are essentially equivalent, where the negation of dop is the property we use in our structure theorem and sdop implies nonstructure, see Hyttinen. Download Export citation Bookmark 23 citations
Generalizing Morley's Theorem.Tapani Hyttinen - 1998 - Mathematical Logic Quarterly 44 (2):176-184.details We study the categoricity of the classes of elementary submodels of a homogeneous structure. Download Export citation Bookmark 12 citations
Groups of small Morley rank.Gregory Cherlin - 1979 - Annals of Mathematical Logic 17 (1):1.details Download Export citation Bookmark 36 citations

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