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.
03A05 Philosophical and critical {For philosophy of mathematics, see also 00A30}
03Bxx General logic
03B05 Classical propositional logic
03B10 Classical first-order logic
03B15 Higher-order logic and type theory
03B20 Subsystems of classical logic (including intuitionistic logic)
03B22 Abstract deductive systems
03B25 Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]
03B30 Foundations of classical theories (including reverse mathematics) [See also 03F35]
03B35 Mechanization of proofs and logical operations [See also 68T15]
03B40 Combinatory logic and lambda-calculus [See also 68N18]
03B42 Logic of knowledge and belief
03B44 Temporal logic
03B45 Modal logic {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects, see 03F52}
03B48 Probability and inductive logic [See also 60A05]
03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]
03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)
03B55 Intermediate logics
03B60 Other nonclassical logic
03B65 Logic of natural languages [See also 68T50, 91F20]
03B70 Logic in computer science [See also 68-XX]
03B80 Other applications of logic
03B99 None of the above, but in this section
03Cxx Model theory
03C05 Equational classes, universal algebra [See also 08Axx, 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, 12Lxx, 13L05]
03C62 Models of arithmetic and set theory [See also 03Hxx]
03C64 Model theory of ordered structures; o-minimality
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]
03C99 None of the above, but in this section
03Dxx Computability and recursion theory
03D03 Thue and Post systems, etc.
03D05 Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]
03D10 Turing machines and related notions [See also 68Q05]
03D15 Complexity of computation [See also 68Q15, 68Q17]
03D20 Recursive functions and relations, subrecursive hierarchies
03D25 Recursively (computably) enumerable sets and degrees
03D28 Other Turing degree structures
03D30 Other degrees and reducibilities
03D35 Undecidability and degrees of sets of sentences
03D40 Word problems, etc. [See also 06B25, 08A50, 20F10]
03D45 Theory of numerations, effectively presented structures [See also 03C57] {For intuitionistic and similar approaches, see 03F55}
03D50 Recursive equivalence types of sets and structures, isols
03D55 Hierarchies
03D60 Computability and recursion theory on ordinals, admissible sets, etc.
03D65 Higher-type and set recursion theory
03D70 Inductive definability
03D75 Abstract and axiomatic computability and recursion theory
03D80 Applications of computability and recursion theory
03D99 None of the above, but in this section
03Exx Set theory
03E02 Partition relations
03E04 Ordered sets and their cofinalities; pcf theory
03E05 Other combinatorial set theory
03E10 Ordinal and cardinal numbers
03E15 Descriptive set theory [See also 28A05, 54H05]
03E17 Cardinal characteristics of the continuum
03E20 Other classical set theory (including functions, relations, and set algebra)
03E25 Axiom of choice and related propositions
03E30 Axiomatics of classical set theory and its fragments
03E35 Consistency and independence results
03E40 Other aspects of forcing and Boolean-valued models
03E45 Inner models, including constructibility, ordinal definability, and core models
03E47 Other notions of set-theoretic definability
03E50 Continuum hypothesis and Martin's axiom
03E55 Large cardinals
03E60 Determinacy principles
03E65 Other hypotheses and axioms
03E70 Nonclassical and second-order set theories
03E72 Fuzzy set theory
03E75 Applications of set theory
03E99 None of the above, but in this section
03Fxx Proof theory and constructive mathematics
03F03 Proof theory, general
03F05 Cut-elimination and normal-form theorems
03F07 Structure of proofs
03F10 Functionals in proof theory
03F15 Recursive ordinals and ordinal notations
03F20 Complexity of proofs
03F25 Relative consistency and interpretations
03F30 First-order arithmetic and fragments
03F35 Second- and higher-order arithmetic and fragments [See also 03B30]
03F40 G\"odel numberings in proof theory
03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]
03F50 Metamathematics of constructive systems
03F52 Linear logic and other substructural logics [See also 03B47]
03F55 Intuitionistic mathematics
03F60 Constructive and recursive analysis [See also 03B30, 03D45, 26E40, 46S30, 47S30]
03F65 Other constructive mathematics [See also 03D45]
03F99 None of the above, but in this section
03Gxx Algebraic logic
03G05 Boolean algebras [See also 06Exx]
03G10 Lattices and related structures [See also 06Bxx]
03G12 Quantum logic [See also 06C15, 81P10]
03G15 Cylindric and polyadic algebras; relation algebras
03G20 Lukasiewicz and Post algebras [See also 06D25, 06D30]
03G25 Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
03G30 Categorical logic, topoi [See also 18B25, 18C05, 18C10]
03G99 None of the above, but in this section
03Hxx Nonstandard models [See also 03C62]
03H05 Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]
03H10 Other applications of nonstandard models (economics, physics, etc.)
03H15 Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]
03H99 None of the above, but in this section