Ranks and pregeometries in finite diagrams

DOI10.1016/S0168-0072(99)00045-7zbMath0969.03048arXivmath/9704206MaRDI QIDQ1591202

Olivier Lessmann

Publication date: 3 October 2001

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9704206

zbMATH Keywords

rankforkingprime modelscategoricityclassification theoryhomogeneous modeltwo-cardinal theoremregular typedependence relationpregeometriesgeneral diagramsstationary typetotally transcendental diagrams

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Other infinitary logic (03C75) Categoricity and completeness of theories (03C35)

Related Items (9)

Shelah's eventual categoricity conjecture in universal classes. I. ⋮ Shelah's eventual categoricity conjecture in tame abstract elementary classes with primes ⋮ INTERPRETING GROUPS AND FIELDS IN SOME NONELEMENTARY CLASSES ⋮ Categoricity and U-rank in excellent classes ⋮ Forking in short and tame abstract elementary classes ⋮ Main gap for locally saturated elementary submodels of a homogeneous structure ⋮ A rank for the class of elementary submodels of a superstable homogeneous model ⋮ Shelah's categoricity conjecture from a successor for tame abstract elementary classes ⋮ Uncountably categorical local tame abstract elementary classes with disjoint amalgamation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)
• Categoricity of theories in \(L_{\kappa \omega}\), with \(\kappa\) a compact cardinal
• A survey of basic stability theory, with particular emphasis on orthogonality and regular types
• Second-order quantifiers and the complexity of theories
• The primal framework. II: Smoothness
• Classification theory and the number of non-isomorphic models.
• Categoricity in \(\aleph_1\) of sentences in \(L_{\omega_1\omega}(Q)\)
• Shelah's stability spectrum and homogeneity spectrum in finite diagrams
• The primal framework. I
• Strong splitting in stable homogeneous models
• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• A combinatorial problem; stability and order for models and theories in infinitary languages
• Indiscernible sequences in a model which fails to have the order property
• On chains of relatively saturated submodels of a model without the order property
• The classification of excellent classes
• On the number of nonisomorphic models of an infinitary theory which has the infinitary order property. Part A
• Countable models of ω1-categorical theories in admissible languages
• One hundred and two problems in mathematical logic
• Abstract classes with few models have ‘homogeneous-universal’ models
• Categoricity in Power
• Finite diagrams stable in power
• On strongly minimal sets
• Categoricity of an abstract elementary class in two successive cardinals

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