Abstract elementary classes and infinitary logics

DOI10.1016/j.apal.2008.07.002zbMath1155.03016OpenAlexW2052439147MaRDI QIDQ998315

David W. Kueker

Publication date: 28 January 2009

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

Full work available at URL: https://doi.org/10.1016/j.apal.2008.07.002

zbMATH Keywords

infinitary logicabstract elementary class

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Properties of classes of models (03C52) Other infinitary logic (03C75) Set-theoretic model theory (03C55) Categoricity and completeness of theories (03C35)

Related Items (14)

Infinitary stability theory ⋮ Kaplansky classes, finite character and ℵ1-projectivity ⋮ ALMOST GALOIS ω-STABLE CLASSES ⋮ Categoricity transfer in simple finitary abstract elementary classes ⋮ A note on the axioms for Zilber's pseudo-exponential fields ⋮ Axiomatizing AECs and applications ⋮ Iterated elementary embeddings and the model theory of infinitary logic ⋮ Interpreting groups and fields in simple, finitary AECs ⋮ Structural logic and abstract elementary classes with intersections ⋮ Shelah's eventual categoricity conjecture in universal classes. II ⋮ Abstract elementary classes and accessible categories ⋮ Abstract elementary classes induced by tilting and cotilting modules have finite character ⋮ CLASSIFICATION THEORY FOR ACCESSIBLE CATEGORIES ⋮ Coxeter groups and abstract elementary classes: the right-angled case

Cites Work

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• Abstract elementary classes with Löwenheim-Skolem number cofinal with \(\omega \)
• Categoricity for abstract classes with amalgamation
• Independence in finitary abstract elementary classes
• Categoricity transfer in simple finitary abstract elementary classes
• Countable approximations and Löwenheim-Skolem theorems
• Shelah's categoricity conjecture from a successor for tame abstract elementary classes
• Some combinatorial problems concerning uncountable cardinals
• Löwenheim-Skolem and interpolation theorems in infinitary languages

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