| 03-XX | | Prev: 01 | Up: Top | Next: 05 | |
| Mathematical logic and foundations [xref: 18A15, 18B05] |
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}
[xref: 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]
[xref: 11U05, 12L05, 20F10]
| 03B30 |
Foundations of classical theories (including reverse mathematics) [See also 03F35]
[xref: 03F35, 03F60]
| 03B35 |
Mechanization of proofs and logical operations [See also 68T15]
[xref: 68T15]
| 03B40 |
Combinatory logic and lambda-calculus [See also 68N18]
[xref: 68N18]
| 03B42 |
Logic of knowledge and belief
[xref: 03C80]
| 03B44 |
Temporal logic
[xref: 03C80]
| 03B45 |
Modal logic {For knowledge and belief see 03B42; for temporal logic see 03B44; for provability logic see also 03F45}
[xref: 03C80, 03F45]
| 03B47 |
Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
[xref: 03F52]
| 03B48 |
Probability and inductive logic [See also 60A05]
[xref: 03C80]
| 03B50 |
Many-valued logic
| 03B52 |
Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]
[xref: 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]
[xref: 68T50, 91F20]
| 03B70 |
Logic in computer science [See also 68-XX]
[xref: 68Q55, 68Q60]
| 03B80 |
Other applications of logic
| 03B99 |
None of the above, but in this section
| |
03Cxx |
Model theory
[xref: 08C10, 11U09, 13L05, 16B70]
| 03C05 |
Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]
[xref: 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]
[xref: 68Q19]
| 03C15 |
Denumerable structures
| 03C20 |
Ultraproducts and related constructions
[xref: 11U07, 12L10]
| 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]
[xref: 03D45]
| 03C60 |
Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
[xref: 03C98, 12L12]
| 03C62 |
Models of arithmetic and set theory [See also 03Hxx]
[xref: 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
[xref: 05A30]
| 03D03 |
Thue and Post systems, etc.
| 03D05 |
Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]
[xref: 18B20, 20F10, 20M35, 68Q45]
| 03D10 |
Turing machines and related notions [See also 68Q05]
[xref: 68Q05]
| 03D15 |
Complexity of computation [See also 68Q15, 68Q17]
[xref: 68Q15]
| 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, 68R15]
[xref: 06B25, 08A50, 20F10]
| 03D45 |
Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
[xref: 03C57, 03F60, 03F65]
| 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
[xref: 54A25]
| 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]
[xref: 26A21, 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
[xref: 54A35]
| 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
[xref: 20N25, 26E50, 28E10, 46S40, 47S40, 54A40, 94D05]
| 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]
[xref: 03B30]
| 03F40 |
Gödel numberings in proof theory
| 03F45 |
Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]
[xref: 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]
[xref: 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]
[xref: 06Exx]
| 03G10 |
Lattices and related structures [See also 06Bxx]
[xref: 06Bxx]
| 03G12 |
Quantum logic [See also 06C15, 81P10]
[xref: 06C15, 81P10]
| 03G15 |
Cylindric and polyadic algebras; relation algebras
| 03G20 |
Lukasiewicz and Post algebras [See also 06D25, 06D30]
[xref: 06D25, 06D30]
| 03G25 |
Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
[xref: 03F45, 06D20, 06E25, 06F35]
| 03G30 |
Categorical logic, topoi [See also 18B25, 18C05, 18C10]
[xref: 18B25, 18C10]
| 03G99 |
None of the above, but in this section
| |
03Hxx |
Nonstandard models [See also 03C62]
[xref: 03C62, 13L05]
| 03H05 |
Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]
[xref: 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]
[xref: 11U10, 12L15]
Other nonstandard models
| 03H99 |
None of the above, but in this section
| |