03XX

Mathematical logic and foundations

0300

General reference works (handbooks, dictionaries, bibliographies, etc.)

0301

Instructional exposition (textbooks, tutorial papers, etc.)

0302

Research exposition (monographs, survey articles)

0303

Historical {!must also be assigned at least one classification number from section 01}

0304

Explicit machine computation and programs (not the theory of computation or programming)

0306

Proceedings, conferences, collections, etc.

03A05

Philosophical and critical
{For philosophy of mathematics, see also
00A30}

03Bxx

General logic

03B05

Classical propositional logic

03B10

Classical firstorder logic

03B15

Higherorder 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 lambdacalculus
[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 prooftheoretic aspects, see
03F52}

03B48

Probability and inductive logic
[See also
60A05]

03B50

Manyvalued 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
68XX]

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 firstorder 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

Modeltheoretic 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

Settheoretic model theory

03C57

Effective and recursiontheoretic model theory
[See also
03D45]

03C60

Modeltheoretic algebra
[See also
08C10,
12Lxx,
13L05]

03C62

Models of arithmetic and set theory
[See also
03Hxx]

03C64

Model theory of ordered structures; ominimality

03C65

Models of other mathematical theories

03C68

Other classical firstorder 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 higherorder model theory

03C90

Nonclassical models (Booleanvalued, 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

Highertype 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 Booleanvalued models

03E45

Inner models, including constructibility, ordinal definability, and core models

03E47

Other notions of settheoretic definability

03E50

Continuum hypothesis and Martin's axiom

03E55

Large cardinals

03E60

Determinacy principles

03E65

Other hypotheses and axioms

03E70

Nonclassical and secondorder 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

Cutelimination and normalform 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

Firstorder arithmetic and fragments

03F35

Second and higherorder 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
