Abstract elementary classes stable in \(\aleph_{0}\)

DOI10.1016/j.apal.2018.02.004zbMath1469.03099arXiv1702.08281OpenAlexW2591586941MaRDI QIDQ2636519

Saharon Shelah, Sebastien Vasey

Publication date: 5 June 2018

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

Full work available at URL: https://arxiv.org/abs/1702.08281

zbMATH Keywords

localityabstract elementary classesgood frames\(\aleph_0\)-stabilitysuperlimit

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Other infinitary logic (03C75) Set-theoretic model theory (03C55) Abstract elementary classes and related topics (03C48)

Related Items (6)

STABILITY RESULTS ASSUMING TAMENESS, MONSTER MODEL, AND CONTINUITY OF NONSPLITTING ⋮ EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES ⋮ Axiomatizing AECs and applications ⋮ UNIVERSAL CLASSES NEAR ${\aleph _1}$ ⋮ Simple-like independence relations in abstract elementary classes ⋮ The categoricity spectrum of large abstract elementary classes

Cites Work

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• Quasiminimal structures, groups and Zariski-like geometries
• Canonical forking in AECs
• Infinitary stability theory
• Building independence relations in abstract elementary classes
• Superstability and symmetry
• A note on the axioms for Zilber's pseudo-exponential fields
• Chains of saturated models in AECs
• Symmetry in abstract elementary classes with amalgamation
• Downward categoricity from a successor inside a good frame
• Categoricity over P for first order T or categoricity for \(\phi\) \(\in {\mathcal L}_{\omega_ 1\omega}\) can stop at \(\aleph_ k\) while holding for \(\aleph_ 0,\dots ,\aleph_{k-1}\)
• Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)
• Iterated elementary embeddings and the model theory of infinitary logic
• Categoricity in \(\aleph_1\) of sentences in \(L_{\omega_1\omega}(Q)\)
• Toward categoricity for classes with no maximal models
• Quasiminimal abstract elementary classes
• Non-forking frames in abstract elementary classes
• Independence in finitary abstract elementary classes
• Categoricity in abstract elementary classes with no maximal models
• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• Uniqueness of limit models in classes with amalgamation
• ALMOST GALOIS ω-STABLE CLASSES
• Examples of non-locality
• EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES
• Simple homogeneous models
• TAMENESS AND FRAMES REVISITED
• The stationary set splitting game
• Quasiminimal structures and excellence
• GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES
• Upward categoricity from a successor cardinal for tame abstract classes with amalgamation
• Symmetry and the union of saturated models in superstable abstract elementary classes

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