Categoricity in \(\aleph_1\) of sentences in \(L_{\omega_1\omega}(Q)\)

DOI10.1007/BF02757882zbMath0324.02038MaRDI QIDQ1224580

Saharon Shelah

Publication date: 1975

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Model theory (03C99) Logic with extra quantifiers and operators (03C80) Other infinitary logic (03C75) Categoricity and completeness of theories (03C35)

Related Items

Shelah's eventual categoricity conjecture in universal classes. I., Canonical forking in AECs, CATEGORICITY FROM ONE SUCCESSOR CARDINAL IN TAME ABSTRACT ELEMENTARY CLASSES, Simplicity and uncountable categoricity in excellent classes, ALMOST GALOIS ω-STABLE CLASSES, Abstract elementary classes stable in \(\aleph_{0}\), Good frames in the Hart-Shelah example, On universal locally finite groups, Iterated elementary embeddings and the model theory of infinitary logic, Uncountable categoricity of local abstract elementary classes with amalgamation, The number of subdirectly irreducible algebras in a variety. II, INTERPRETING GROUPS AND FIELDS IN SOME NONELEMENTARY CLASSES, Canonical bases in excellent classes, HENKIN CONSTRUCTIONS OF MODELS WITH SIZE CONTINUUM, THE NUMBER OF ATOMIC MODELS OF UNCOUNTABLE THEORIES, UNIVERSAL CLASSES NEAR ${\aleph _1}$, Superstability from categoricity in abstract elementary classes, A complete L_ω1ω-sentence characterizing ℵ₁, Notes on Quasiminimality and Excellence, Categoricity in abstract elementary classes with no maximal models, Three red herrings around Vaught’s conjecture, An inelastic model with indiscernibles, Prime and atomic models, FORKING AND SUPERSTABILITY IN TAME AECS, 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 \(\aleph_ 0,\dots ,\aleph_{k-1}\), Categoricity for abstract classes with amalgamation, Ranks and pregeometries in finite diagrams, Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)

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