Categoricity in homogeneous complete metric spaces

DOI10.1007/s00153-009-0120-zzbMath1181.03039OpenAlexW2048044535MaRDI QIDQ1016502

Tapani Hyttinen, Åsa Hirvonen

Publication date: 6 May 2009

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-009-0120-z

zbMATH Keywords

Banach spaceshomogeneitycategoricity transfer theoremmetric abstract elementary classmodel theory of metric structures

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Classification theory, stability, and related concepts in model theory (03C45) Properties of classes of models (03C52) Applications of model theory (03C98) Categoricity and completeness of theories (03C35) Abstract elementary classes and related topics (03C48)

Related Items

Reduction of database independence to dividing in atomless Boolean algebras ⋮ Model theory of a Hilbert space expanded with an unbounded closed selfadjoint operator ⋮ A presentation theorem for continuous logic and metric abstract elementary classes ⋮ METRIC ABSTRACT ELEMENTARY CLASSES AS ACCESSIBLE CATEGORIES ⋮ Sizes and filtrations in accessible categories ⋮ Tameness in generalized metric structures ⋮ 2010 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '10 ⋮ Universal abstract elementary classes and locally multipresentable categories ⋮ TAMENESS FROM LARGE CARDINAL AXIOMS ⋮ Convex-transitivity and function spaces ⋮ Sheaves of Metric Structures ⋮ Approximate injectivity and smallness in metric-enriched categories ⋮ THE KIM–PILLAY THEOREM FOR ABSTRACT ELEMENTARY CATEGORIES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Model theoretic stability and categoricity for complete metric spaces
• Classification theory and the number of non-isomorphic models.
• When do two Banach spaces have isometrically isomorphic nonstandard hulls
• Nonstandard hulls of Banach spaces
• Categoricity for abstract classes with amalgamation
• Three-space problems in Banach space theory
• Espaces de Banach stables
• Simple stable homogeneous expansions of Hilbert spaces
• Strong splitting in stable homogeneous models
• Metric abstract elementary classes with perturbations
• Continuous first order logic and local stability
• On perturbations of Hilbert spaces and probability algebras with a generic automorphism
• Universal relational systems
• On d-finiteness in continuous structures
• On the maximality of logics with approximations
• POSITIVE MODEL THEORY AND COMPACT ABSTRACT THEORIES
• Simple homogeneous models
• Application des ultraproduits à l'étude des espaces et des algèbres de Banach
• ON PERTURBATIONS OF CONTINUOUS STRUCTURES
• Continuous Model Theory. (AM-58)
• Homogeneous Universal Relational Systems.
• Finite diagrams stable in power
• Uncountable dense categoricity in cats