FORKING AND SUPERSTABILITY IN TAME AECS

DOI10.1017/JSL.2015.51zbMath1431.03049arXiv1405.7443OpenAlexW3104393925MaRDI QIDQ2805041

Sebastien Vasey

Publication date: 9 May 2016

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7443

zbMATH Keywords

independencestabilitystability spectrumforkingcategoricitytamenesssuperstabilityabstract 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 (23)

Shelah's eventual categoricity conjecture in universal classes. I. ⋮ \(\mu\)-abstract elementary classes and other generalizations ⋮ Canonical forking in AECs ⋮ Building independence relations in abstract elementary classes ⋮ 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 ⋮ Building prime models in fully good abstract elementary classes ⋮ On the uniqueness property of forking in abstract elementary classes ⋮ STABILITY RESULTS ASSUMING TAMENESS, MONSTER MODEL, AND CONTINUITY OF NONSPLITTING ⋮ Shelah's eventual categoricity conjecture in tame abstract elementary classes with primes ⋮ TAMENESS AND FRAMES REVISITED ⋮ EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES ⋮ 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 ⋮ Downward categoricity from a successor inside a good frame ⋮ Non-forking w-good frames ⋮ The categoricity spectrum of large abstract elementary classes ⋮ Algebraic description of limit models in classes of abelian groups

Cites Work

• Unnamed Item
• Upward stability transfer for tame abstract elementary classes
• Categoricity in \(\aleph_1\) of sentences in \(L_{\omega_1\omega}(Q)\)
• Categoricity for abstract classes with amalgamation
• Toward categoricity for classes with no maximal models
• Non-forking frames in abstract elementary classes
• Categoricity in abstract elementary classes with no maximal models
• CATEGORICITY FROM ONE SUCCESSOR CARDINAL IN TAME ABSTRACT ELEMENTARY CLASSES
• Tameness and extending frames
• GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES
• Categoricity of an abstract elementary class in two successive cardinals

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