Categoricity in abstract elementary classes with no maximal models

DOI10.1016/j.apal.2005.10.006zbMath1106.03031arXivmath/0510579OpenAlexW2040052675MaRDI QIDQ2498904

Monica Van Dieren

Publication date: 16 August 2006

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

Full work available at URL: https://arxiv.org/abs/math/0510579

zbMATH Keywords

abstract elementary classesShelah's categoricity conjectureuniqueness of limit models

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Properties of classes of models (03C52) Categoricity and completeness of theories (03C35) Abstract elementary classes and related topics (03C48)

Related Items (32)

Shelah's eventual categoricity conjecture in universal classes. I. ⋮ Canonical forking in AECs ⋮ CATEGORICITY FROM ONE SUCCESSOR CARDINAL IN TAME ABSTRACT ELEMENTARY CLASSES ⋮ Building independence relations in abstract elementary classes ⋮ Abstract elementary classes stable in \(\aleph_{0}\) ⋮ Superstability and symmetry ⋮ Toward a stability theory of tame abstract elementary classes ⋮ Good frames in the Hart-Shelah example ⋮ ON CATEGORICITY IN SUCCESSIVE CARDINALS ⋮ Saturation and solvability in abstract elementary classes with amalgamation ⋮ On the uniqueness property of forking in abstract elementary classes ⋮ STABILITY RESULTS ASSUMING TAMENESS, MONSTER MODEL, AND CONTINUITY OF NONSPLITTING ⋮ EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES ⋮ Uncountable categoricity of local abstract elementary classes with amalgamation ⋮ Category-theoretic aspects of abstract elementary classes ⋮ Superstability, Noetherian rings and pure-semisimple rings ⋮ Superstability from categoricity in abstract elementary classes ⋮ Chains of saturated models in AECs ⋮ Symmetry in abstract elementary classes with amalgamation ⋮ Forking in short and tame abstract elementary classes ⋮ Tameness and extending frames ⋮ TAMENESS FROM LARGE CARDINAL AXIOMS ⋮ Simple-like independence relations in abstract elementary classes ⋮ Downward categoricity from a successor inside a good frame ⋮ Symmetry and the union of saturated models in superstable abstract elementary classes ⋮ FORKING AND SUPERSTABILITY IN TAME AECS ⋮ Limit models in metric abstract elementary classes: the categorical case ⋮ Uniqueness of limit models in classes with amalgamation ⋮ GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES ⋮ On superstability in the class of flat modules and perfect rings ⋮ The categoricity spectrum of large abstract elementary classes ⋮ Algebraic description of limit models in classes of abelian groups

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