Mathematics Subject Classification – History and Foundations

HISTORY AND BIOGRAPHY

AMS: 01 All of this section
AMS: 01-XX Not classified at a more specific level

AMS: 01-00 General reference works
AMS: 01-01 Instructional exposition
AMS: 01-02 Research exposition
AMS: 01-06 Proceedings, conferences, collections, etc.
AMS: 01-08 Computational methods

AMS: 01Axx History of mathematics and mathematicians
AMS: 01A* (including sub-levels)
- AMS: 01A05 General histories, source books
- AMS: 01A07 Ethnomathematics, general
- AMS: 01A12 Indigenous cultures of the Americas
- AMS: 01A15 Indigenous European cultures (pre-Greek, etc.)
- AMS: 01A16 Egyptian
- AMS: 01A17 Babylonian
- AMS: 01A20 Greek, Roman
- AMS: 01A25 China
- AMS: 01A30 Islam (Medieval)
- AMS: 01A32 India
- AMS: 01A35 Medieval
- AMS: 01A40 15th and 16th centuries, Renaissance
- AMS: 01A45 17th century
- AMS: 01A50 18th century
- AMS: 01A55 19th century
- AMS: 01A60 20th century
- AMS: 01A61 Twenty-first century
- AMS: 01A65 Contemporary
- AMS: 01A67 Future prospectives
- AMS: 01A70 Biographies, obituaries, personalia, bibliographies
- AMS: 01A72 Schools of mathematics
- AMS: 01A73 Universities
- AMS: 01A75 Collected or selected works; reprintings or translations of classics
- AMS: 01A80 Sociology (and profession) of mathematics
- AMS: 01A85 Historiography
- AMS: 01A90 Bibliographic studies
- AMS: 01A99 Miscellaneous topics

MATHEMATICAL LOGIC AND FOUNDATIONS

AMS: 03 All of this section
AMS: 03-XX Not classified at a more specific level

AMS: 03-00 General reference works
AMS: 03-01 Instructional exposition
AMS: 03-02 Research exposition
AMS: 03-03 Historical
AMS: 03-04 Explicit machine computation and programs
AMS: 03-06 Proceedings, conferences, collections, etc.

AMS: 03Axx Philosophical aspects of logic and foundations
AMS: 03A* (including sub-levels)
- AMS: 03A05 Philosophical and critical
- AMS: 03A99 None of the above, but in this section
AMS: 03Bxx General logic
AMS: 03B* (including sub-levels)
- AMS: 03B05 Classical propositional logic
- AMS: 03B10 Classical first-order logic
- AMS: 03B15 Higher-order logic and type theory
- AMS: 03B25 Decidability of theories and sets of sentences
- AMS: 03B30 Foundations of classical theories (including reverse mathematics)
- AMS: 03B35 Mechanization of proofs and logical operations
- AMS: 03B45 Modal logic
- AMS: 03B48 Probability and inductive logic
- AMS: 03B50 Many-valued logic
- AMS: 03B52 Fuzzy logic; logic of vagueness
- AMS: 03B60 Other nonclassical logic
- AMS: 03B65 Logic of natural languages
- AMS: 03B70 Logic in computer science
- AMS: 03B99 None of the above, but in this section
AMS: 03Cxx Model theory
AMS: 03C* (including sub-levels)
- AMS: 03C05 Equational classes, universal algebra
- AMS: 03C07 Basic properties of first-order languages and structures
- AMS: 03C13 Finite structures
- AMS: 03C20 Ultraproducts and related constructions
- AMS: 03C25 Model-theoretic forcing
- AMS: 03C35 Categoricity and completeness of theories
- AMS: 03C45 Classification theory, stability and related concepts
- AMS: 03C52 Properties of classes of models
- AMS: 03C55 Set-theoretic model theory
- AMS: 03C57 Effective and recursion-theoretic model theory
- AMS: 03C60 Model-theoretic algebra
- AMS: 03C62 Models of arithmetic and set theory
- AMS: 03C64 Model theory of ordered structures; o-minimality
- AMS: 03C65 Models of other mathematical theories
- AMS: 03C80 Logic with extra quantifiers and operators
- AMS: 03C95 Abstract model theory
- AMS: 03C98 Applications of model theory
- AMS: 03C99 None of the above, but in this section
AMS: 03Dxx Computability and recursion theory
AMS: 03D* (including sub-levels)
- AMS: 03D05 Automata and formal grammars in connection with logical questions
- AMS: 03D10 Turing machines and related notions
- AMS: 03D15 Complexity of computation
- AMS: 03D20 Recursive functions and relations, subrecursive hierarchies
- AMS: 03D25 Recursively (computably) enumerable sets and degrees
- AMS: 03D28 Other Turing degree structures
- AMS: 03D30 Other degrees and reducibilities
- AMS: 03D35 Undecidability and degrees of sets of sentences
- AMS: 03D40 Word problems, etc.
- AMS: 03D45 Theory of numerations, effectively presented structures
- AMS: 03D50 Recursive equivalence types of sets and structures, isols
- AMS: 03D55 Hierarchies
- AMS: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.
- AMS: 03D65 Higher-type and set recursion theory
- AMS: 03D75 Abstract and axiomatic computability and recursion theory
- AMS: 03D80 Applications of computability and recursion theory
AMS: 03Exx Set theory
AMS: 03E* (including sub-levels)
- AMS: 03E05 Other combinatorial set theory
- AMS: 03E10 Ordinal and cardinal numbers
- AMS: 03E15 Descriptive set theory
- AMS: 03E17 Cardinal characteristics of the continuum
- AMS: 03E20 Other classical set theory (including functions, relations, and set algebra)
- AMS: 03E25 Axiom of choice and related propositions
- AMS: 03E30 Axiomatics of classical set theory and its fragments
- AMS: 03E35 Consistency and independence results
- AMS: 03E40 Other aspects of forcing and Boolean-valued models
- AMS: 03E45 Inner models, including constructibility, ordinal definability, and core models
- AMS: 03E47 Other notions of set-theoretic definability
- AMS: 03E50 Continuum hypothesis and Martin's axiom
- AMS: 03E55 Large cardinals
- AMS: 03E60 Determinacy principles
- AMS: 03E70 Nonclassical and second-order set theories
- AMS: 03E72 Fuzzy set theory
- AMS: 03E75 Applications of set theory
- AMS: 03E99 None of the above, but in this section
AMS: 03Fxx Proof theory and constructive mathematics
AMS: 03F* (including sub-levels)
- AMS: 03F20 Complexity of proofs
- AMS: 03F30 First-order arithmetic and fragments
- AMS: 03F35 Second- and higher-order arithmetic and fragments
- AMS: 03F50 Metamathematics of constructive systems
- AMS: 03F55 Intuitionistic mathematics
- AMS: 03F60 Constructive and recursive analysis
- AMS: 03F65 Other constructive mathematics
- AMS: 03F99 None of the above, but in this section
AMS: 03Gxx Algebraic logic
AMS: 03G* (including sub-levels)
- AMS: 03G05 Boolean algebras
- AMS: 03G10 Lattices and related structures
- AMS: 03G12 Quantum logic
- AMS: 03G15 Cylindric and polyadic algebras; relation algebras
- AMS: 03G30 Categorical logic, topoi
- AMS: 03G99 None of the above, but in this section
AMS: 03Hxx Nonstandard models
AMS: 03H* (including sub-levels)
- AMS: 03H05 Nonstandard models in mathematics
- AMS: 03H10 Other applications of nonstandard models (economics, physics, etc.)
- AMS: 03H15 Nonstandard models of arithmetic

COMBINATORICS

AMS: 05 All of this section
AMS: 05-XX Not classified at a more specific level

AMS: 05-00 General reference works
AMS: 05-01 Instructional exposition
AMS: 05-02 Research exposition
AMS: 05-03 Historical
AMS: 05-06 Proceedings, conferences, collections, etc.

AMS: 05Axx Enumerative combinatorics
AMS: 05A* (including sub-levels)
- AMS: 05A05 Combinatorial choice problems (subsets, representatives, permutations)
- AMS: 05A10 Factorials, binomial coefficients, combinatorial functions
- AMS: 05A15 Exact enumeration problems, generating functions Asymptotic enumeration
- AMS: 05A17 Partitions of integers
- AMS: 05A19 Combinatorial identities
- AMS: 05A20 Combinatorial inequalities
- AMS: 05A30 $q$-calculus and related topics
- AMS: 05A40 Umbral calculus
AMS: 05Bxx Designs and configurations
AMS: 05B* (including sub-levels)
- AMS: 05B05 Block designs
- AMS: 05B10 Difference sets (number-theoretic, group-theoretic, etc.)
- AMS: 05B15 Orthogonal arrays, Latin squares, Room squares
- AMS: 05B20 Matrices (incidence, Hadamard, etc.)
- AMS: 05B25 Finite geometries
- AMS: 05B30 Other designs, configurations
- AMS: 05B35 Matroids, geometric lattices
- AMS: 05B40 Packing and covering
- AMS: 05B45 Tessellation and tiling problems
- AMS: 05B99 None of the above, but in this section
AMS: 05Cxx Graph theory
AMS: 05C* (including sub-levels)
- AMS: 05C05 Trees
- AMS: 05C07 Degree sequences
- AMS: 05C10 Topological graph theory, imbedding
- AMS: 05C12 Distance in graphs
- AMS: 05C15 Coloring of graphs and hypergraphs
- AMS: 05C20 Directed graphs (digraphs), tournaments
- AMS: 05C25 Graphs and groups
- AMS: 05C30 Enumeration of graphs and maps
- AMS: 05C35 Extremal problems
- AMS: 05C38 Paths and cycles
- AMS: 05C40 Connectivity
- AMS: 05C45 Eulerian and Hamiltonian graphs
- AMS: 05C50 Graphs and matrices
- AMS: 05C55 Generalized Ramsey theory
- AMS: 05C57 Games on graphs
- AMS: 05C62 Graph representations (geometric and intersection representations, etc.)
- AMS: 05C65 Hypergraphs
- AMS: 05C70 Factorization, matching, covering and packing
- AMS: 05C75 Structural characterization of types of graphs
- AMS: 05C80 Random graphs
- AMS: 05C81 Random walks on graphs
- AMS: 05C85 Graph algorithms
- AMS: 05C90 Applications
- AMS: 05C99 None of the above, but in this section
AMS: 05Dxx Extremal combinatorics
AMS: 05D* (including sub-levels)
- AMS: 05D05 Extremal set theory
- AMS: 05D10 Ramsey theory
- AMS: 05D40 Probabilistic methods
AMS: 05Exx Algebraic combinatorics
AMS: 05E* (including sub-levels)
- AMS: 05E05 Symmetric functions
- AMS: 05E10 Tableaux, representations of the symmetric group
- AMS: 05E15 Combinatorial problems concerning the classical groups
- AMS: 05E30 Association schemes, strongly regular graphs
- AMS: 05E99 None of the above, but in this section

Letzte Änderung: 20.07.2012 Gabriele Dörflinger