|
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
|