Continuous and random Vapnik-Chervonenkis classes

DOI10.1007/s11856-009-0094-xzbMath1184.03020arXiv0802.0068OpenAlexW3103033707MaRDI QIDQ2655764

Itaï Ben Yaacov

Publication date: 26 January 2010

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

Full work available at URL: https://arxiv.org/abs/0802.0068

zbMATH Keywords

randomizationindependence propertycontinuous logicmetric structuresstable theoriesdependent theoriesVapnik-Chervonenkis classes

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Nonclassical models (Boolean-valued, sheaf, etc.) (03C90)

Related Items (13)

RECONSTRUCTION OF NON--CATEGORICAL THEORIES ⋮ Sequential approximations for types and Keisler measures ⋮ MODEL THEORETIC PROPERTIES OF METRIC VALUED FIELDS ⋮ Using ultrapowers to compare continuous structures ⋮ AUTOMORPHISM GROUPS OF RANDOMIZED STRUCTURES ⋮ On theories of random variables ⋮ Thorn-forking in continuous logic ⋮ Finding generically stable measures ⋮ Definable connectedness of randomizations of groups ⋮ LOCAL KEISLER MEASURES AND NIP FORMULAS ⋮ SEPARABLE MODELS OF RANDOMIZATIONS ⋮ Generically stable and smooth measures in NIP theories ⋮ Isometry groups of Borel randomizations

Cites Work

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• Randomizations of models as metric structures
• Nonstandard hulls of Banach spaces
• Randomizing a model
• Espaces de Banach stables
• Vapnik-Chervonenkis Classes of Definable Sets
• POSITIVE MODEL THEORY AND COMPACT ABSTRACT THEORIES
• Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory
• Groups, measures, and the NIP
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities

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