La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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03-XX Mathematical logic and foundations

• 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 03-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 03-02 Research exposition (monographs, survey articles)
• 03-03 Historical (must also be assigned at least one classification number from Section 01)
• 03-04 Explicit machine computation and programs (not the theory of computation or programming)
• 03-06 Proceedings, conferences, collections, etc.
• 03-99 Mathematical logic and foundations (not classified at a more specific level)
• 03A05 Philosophical and critical [For philosophy of mathematics, see also 00A30]
• 03Bxx General logic
• 03Cxx Model theory
  • 03C05 Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]
  • 03C07 Basic properties of first-order languages and structures
  • 03C10 Quantifier elimination, model completeness and related topics
  • 03C13 Finite structures [See also 68Q15, 68Q19]
  • 03C15 Denumerable structures
  • 03C20 Ultraproducts and related constructions
  • 03C25 Model-theoretic forcing
  • 03C30 Other model constructions
  • 03C35 Categoricity and completeness of theories
  • 03C40 Interpolation, preservation, definability
  • 03C45 Classification theory, stability and related concepts
  • 03C50 Models with special properties (saturated, rigid, etc.)
  • 03C52 Properties of classes of models
  • 03C55 Set-theoretic model theory
  • 03C57 Effective and recursion-theoretic model theory [See also 03D45]
  • 03C60 Model-theoretic algebra [See also 08C10, 11U09, 12L12, 13L05, 16B70, 20A15]
  • 03C62 Models of arithmetic and set theory [See also 03Hxx]
  • 03C64 Model theory of ordered structures; o-minimality [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 03C40, 03C45, 03C50, 03C60
  • 03C65 Models of other mathematical theories
  • 03C68 Other classical first-order model theory
  • 03C70 Logic on admissible sets
  • 03C75 Other infinitary logic
  • 03C80 Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]
  • 03C85 Second- and higher-order model theory
  • 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
  • 03C95 Abstract model theory
  • 03C98 Applications of model theory [See also 03C60] [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 03C99
  • 03C99 None of the above, but in this section
• 03Dxx Computability and recursion theory
• 03Exx Set theory
• 03Fxx Proof theory and constructive mathematics
• 03Gxx Algebraic logic
• 03Hxx Nonstandard models [See also 03C62]

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