CATEGORICITY FROM ONE SUCCESSOR CARDINAL IN TAME ABSTRACT ELEMENTARY CLASSES
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Publication:3444856
DOI10.1142/S0219061306000554zbMath1129.03019arXivmath/0510004WikidataQ56689307 ScholiaQ56689307MaRDI QIDQ3444856
Rami Grossberg, Monica Van Dieren
Publication date: 5 June 2007
Published in: Journal of Mathematical Logic (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0510004
Classification theory, stability, and related concepts in model theory (03C45) Properties of classes of models (03C52) Other infinitary logic (03C75) Categoricity and completeness of theories (03C35)
Related Items (35)
Shelah's eventual categoricity conjecture in universal classes. I. ⋮ \(\mu\)-abstract elementary classes and other generalizations ⋮ Canonical forking in AECs ⋮ Infinitary stability theory ⋮ Categoricity, amalgamation, and tameness ⋮ Categoricity transfer in simple finitary abstract elementary classes ⋮ Building independence relations in abstract elementary classes ⋮ A stability transfer theorem in d -tame metric abstract elementary classes ⋮ Superstability and symmetry ⋮ ON CATEGORICITY IN SUCCESSIVE CARDINALS ⋮ Accessible images revisited ⋮ Large cardinal axioms from tameness in AECs ⋮ 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 ⋮ Uncountable categoricity of local abstract elementary classes with amalgamation ⋮ Independence in finitary abstract elementary classes ⋮ Tameness in generalized metric structures ⋮ A topology for galois types in abstract elementary classes ⋮ \(^{\perp}N\) as an abstract elementary class ⋮ Shelah's eventual categoricity conjecture in universal classes. II ⋮ Superstability from categoricity in abstract elementary classes ⋮ Symmetry in abstract elementary classes with amalgamation ⋮ Forking in short and tame abstract elementary classes ⋮ Tameness and extending frames ⋮ TAMENESS FROM LARGE CARDINAL AXIOMS ⋮ Downward categoricity from a successor inside a good frame ⋮ Symmetry and the union of saturated models in superstable abstract elementary classes ⋮ Examples of non-locality ⋮ FORKING AND SUPERSTABILITY IN TAME AECS ⋮ Tameness from two successive good frames ⋮ Uniqueness of limit models in classes with amalgamation ⋮ The categoricity spectrum of large abstract elementary classes ⋮ Algebraic description of limit models in classes of abelian groups ⋮ THE KIM–PILLAY THEOREM FOR ABSTRACT ELEMENTARY CATEGORIES
Cites Work
- Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)
- 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
- Categoricity in abstract elementary classes with no maximal models
- Categoricity of theories in Lκ*, ω, when κ*is a measurable cardinal. Part 2
- Shelah's categoricity conjecture from a successor for tame abstract elementary classes
- GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES
- Upward categoricity from a successor cardinal for tame abstract classes with amalgamation
- Categoricity of an abstract elementary class in two successive cardinals
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