
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


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

03B30 
Foundations of classical theories (including reverse mathematics)
[See also
Foundation and axiomatics of classical theories 
03B35 
Mechanization of proofs and logical operations
[See also

03B40 
Combinatory logic and lambdacalculus
[See also
/:> [See also 
03B42 
Logic of knowledge and belief

03B44 
Temporal logic

03B45 
Modal logic
{For knowledge and belief, see
Modal and tense logic {For provability logic, see also 
03B46 
Relevance and entailment 
03B47 
Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
{For prooftheoretic aspects, see

03B48 
Probability and inductive logic
[See also

03B50 
Manyvalued logic

03B52 
Fuzzy logic; logic of vagueness
[See also
/:> ; Logic of vagueness /:> 
03B53 
Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)
Paraconsistent logic 
03B55 
Intermediate logics

03B60 
Other nonclassical logic

03B65 
Logic of natural languages
[See also
// 
03B70 
Logic in computer science
[See also
Logic of programming [See also 
03B80 
Other applications of logic

03B99 
None of the above, but in this section


Model theory

03C05 
Equational classes, universal algebra
[See also
/:> , 
03C07 
Basic properties of firstorder languages and structures

03C10 
Quantifier elimination, model completeness and related topics
/:> , Model completeness 
03C13 
Finite structures
[See also
/:> [See also 
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
/:> Classification theory 
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
/:> Effective and 
03C60 
Modeltheoretic algebra
[See also

03C62 
Models of arithmetic and set theory
[See also

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
/:> 
03C85 
Second and higherorder model theory

03C90 
Nonclassical models (Booleanvalued, sheaf, etc.)

03C95 
Abstract model theory

03C98 
Applications of model theory
[See also

03C99 
None of the above, but in this section


Computability and recursion theory
/:> Computability and 
03D03 
Thue and Post systems, etc.

03D05 
Automata and formal grammars in connection with logical questions
[See also
// 
03D10 
Turing machines and related notions
[See also

03D15 
Complexity of computation
[See also
/:> 
03D20 
Recursive functions and relations, subrecursive hierarchies

03D25 
Recursively (computably) enumerable sets and degrees
/:> (Computably) 
03D28 
Other Turing degree structures

03D30 
Other degrees and reducibilities

03D35 
Undecidability and degrees of sets of sentences

03D40 
Word problems, etc.
[See also

03D45 
Theory of numerations, effectively presented structures
[See also
/:> {For intuitionistic and similar approaches, see 
03D50 
Recursive equivalence types of sets and structures, isols

03D55 
Hierarchies

03D60 
Computability and recursion theory on ordinals, admissible sets, etc.
/:> Computability and 
03D65 
Highertype and set recursion theory

03D70 
Inductive definability

03D75 
Abstract and axiomatic computability and recursion theory
/:> Computability and 
03D80 
Applications of computability and recursion theory

03D99 
None of the above, but in this section


Set theory
/:< [See also 
03E02 
Partition relations

03E04 
Ordered sets and their cofinalities; pcf theory

03E05 
Other combinatorial set theory
/:< [See also 
03E10 
Ordinal and cardinal numbers
/:< [See also 
03E15 
Descriptive set theory
[See also
/:< 
03E17 
Cardinal characteristics of the continuum

03E20 
Other classical set theory (including functions, relations, and set algebra)
/:> (Including functions, relations, and set algebra) 
03E25 
Axiom of choice and related propositions
/:< [See also 
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
/:> Inner models, including // core models ~ related notions 
03E47 
Other notions of settheoretic definability

03E50 
Continuum hypothesis and Martin's axiom
/:< [See also 
03E55 
Large cardinals

03E60 
Determinacy principles
Determinacy and related principles which contradict the axiom of choice 
03E65 
Other hypotheses and axioms

03E70 
Nonclassical and secondorder set theories

03E72 
Fuzzy set theory
Fuzzy sets [See mainly 
03E75 
Applications of set theory
/:> Of set theory 
03E99 
None of the above, but in this section


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
// 
03F40 
G\"odel numberings in proof theory

03F45 
Provability logics and related algebras (e.g., diagonalizable algebras)
[See also

03F50 
Metamathematics of constructive systems

03F52 
Linear logic and other substructural logics
[See also

03F55 
Intuitionistic mathematics

03F60 
Constructive and recursive analysis
[See also
/:> 
03F65 
Other constructive mathematics
[See also
// 
03F99 
None of the above, but in this section


Algebraic logic

03G05 
Boolean algebras
[See also

03G10 
Lattices and related structures
[See also

03G12 
Quantum logic
[See also
/:> 
03G15 
Cylindric and polyadic algebras; relation algebras

03G20 
Lukasiewicz and Post algebras
[See also

03G25 
Other algebras related to logic
[See also
/:> 
03G30 
Categorical logic, topoi
[See also
/:> 
03G99 
None of the above, but in this section


Nonstandard models
[See also

03H05 
Nonstandard models in mathematics
[See also

03H10 
Other applications of nonstandard models (economics, physics, etc.)

03H15 
Nonstandard models of arithmetic
[See also

03H99 
None of the above, but in this section
