Canonical forking in AECs

DOI10.1016/j.apal.2016.03.004zbMath1400.03060arXiv1404.1494OpenAlexW1903296088MaRDI QIDQ278766

F. Blanchet-Sadri, M. Dambrine

Publication date: 2 May 2016

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

Full work available at URL: https://arxiv.org/abs/1404.1494

zbMATH Keywords

stabilityforkingabstract elementary classesclassification theorygood frames

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Properties of classes of models (03C52) Set-theoretic model theory (03C55) Abstract elementary classes and related topics (03C48)

Related Items (24)

Shelah's eventual categoricity conjecture in universal classes. I. ⋮ Quasiminimal structures, groups and Zariski-like geometries ⋮ Infinitary stability theory ⋮ Building independence relations in abstract elementary classes ⋮ Abstract elementary classes stable in \(\aleph_{0}\) ⋮ Toward a stability theory of tame abstract elementary classes ⋮ Good frames in the Hart-Shelah example ⋮ Saturation and solvability in abstract elementary classes with amalgamation ⋮ CELLULAR CATEGORIES AND STABLE INDEPENDENCE ⋮ Building prime models in fully good abstract elementary classes ⋮ STABILITY RESULTS ASSUMING TAMENESS, MONSTER MODEL, AND CONTINUITY OF NONSPLITTING ⋮ TAMENESS AND FRAMES REVISITED ⋮ EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES ⋮ Forking independence from the categorical point of view ⋮ Shelah's eventual categoricity conjecture in universal classes. II ⋮ Chains of saturated models in AECs ⋮ Symmetry in abstract elementary classes with amalgamation ⋮ Forking in short and tame abstract elementary classes ⋮ Simple-like independence relations in abstract elementary classes ⋮ Downward categoricity from a successor inside a good frame ⋮ Non-forking w-good frames ⋮ Independence in Model Theory ⋮ The categoricity spectrum of large abstract elementary classes ⋮ Hanf number of the first stability cardinal in AECs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Infinitary stability theory
• Building independence relations in abstract elementary classes
• Computing the number of types of infinite length
• Chains of saturated models in AECs
• Symmetry in abstract elementary classes with amalgamation
• Forking in short and tame abstract elementary classes
• Erratum to: ``Categoricity in abstract elementary classes with no maximal models
• Categoricity of theories in \(L_{\kappa \omega}\), with \(\kappa\) a compact cardinal
• Fundamentals of forking
• Classification theory and the number of non-isomorphic models.
• Categoricity in \(\aleph_1\) of sentences in \(L_{\omega_1\omega}(Q)\)
• Ranks and definability in superstable theories
• Categoricity for abstract classes with amalgamation
• Toward categoricity for classes with no maximal models
• Simple theories
• Non-forking frames in abstract elementary classes
• Categoricity in abstract elementary classes with no maximal models
• FORKING AND SUPERSTABILITY IN TAME AECS
• Uniqueness of limit models in classes with amalgamation
• CATEGORICITY FROM ONE SUCCESSOR CARDINAL IN TAME ABSTRACT ELEMENTARY CLASSES
• A GEOMETRIC INTRODUCTION TO FORKING AND THORN-FORKING
• THORN-FORKING AS LOCAL FORKING
• Tameness and extending frames
• TAMENESS FROM LARGE CARDINAL AXIOMS
• Independence, dimension and continuity in non-forking frames
• GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES
• Categoricity of an abstract elementary class in two successive cardinals

This page was built for publication: Canonical forking in AECs