EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES

DOI10.1017/jsl.2017.21zbMath1387.03030arXiv1507.04223OpenAlexW2963191261MaRDI QIDQ4600459

Sebastien Vasey, Rami Grossberg

Publication date: 11 January 2018

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

Full work available at URL: https://arxiv.org/abs/1507.04223

zbMATH Keywords

independencesolvabilitytamenesssuperstabilityabstract elementary classeslimit modelclassification theorygood framesuperlimitsaturatedness

Mathematics Subject Classification ID

Large cardinals (03E55) 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) Abstract elementary classes and related topics (03C48)

Related Items (21)

\(\mu\)-abstract elementary classes and other generalizations ⋮ 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 ⋮ On universal modules with pure embeddings ⋮ The Hanf number in the strictly stable case ⋮ 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 ⋮ A note on torsion modules with pure embeddings ⋮ Superstability, Noetherian rings and pure-semisimple rings ⋮ Superstability from categoricity in abstract elementary classes ⋮ 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 ⋮ 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 ⋮ SOME STABLE NON-ELEMENTARY CLASSES OF MODULES

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