La Classification Mathématique par matières 2000
Mathematics subject Classification 2000
Question : CC = Set
03-XX Mathematical logic and foundations
- 03B25 Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]
- 03C55 Set-theoretic model theory
- 03C62 Models of arithmetic and set theory [See also 03Hxx]
- 03C70 Logic on admissible sets
- 03D25 Recursively (computably) enumerable sets and degrees
- 03D35 Undecidability and degrees of sets of sentences
- 03D50 Recursive equivalence types of sets and structures, isols
- 03D60 Computability and recursion theory on ordinals, admissible sets, etc.
- 03D65 Higher-type and set recursion theory
- 03Exx Set theory
- 03E04 Ordered sets and their cofinalities; pcf theory
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
03E05, 03E10, 04A10, 04A20
- 03E05 Other combinatorial set theory
- 03E15 Descriptive set theory [See also 26A21, 28A05, 54H05]
- 03E20 Other classical set theory (including functions, relations, and set algebra)
- 03E30 Axiomatics of classical set theory and its fragments
- 03E47 Other notions of set-theoretic definability
- 03E70 Nonclassical and second-order set theories
- 03E72 Fuzzy set theory
- 03E75 Applications of set theory
05-XX Combinatorics [For finite fields, see 11Txx]
- 05A05 Combinatorial choice problems (subsets, representatives, permutations)
- 05A18 Partitions of sets
- 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]
- 05C69 Dominating sets, independent sets, cliques
[Nouveau code MSC 2000]
- 05D05 Extremal set theory
- 05E25 Group actions on posets and homology groups of posets [See also 06A11]
06-XX Order, lattices, ordered algebraic structures [See also 18B35]
- 06Axx Ordered sets
- 06A07 Combinatorics of partially ordered sets
- 06A11 Algebraic aspects of posets [See also 05E25, 52B20]
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
06A08, 06A09
- 06B35 Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 54F05, 68Q55]
- 06C15 Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]
11-XX Number theory
14-XX Algebraic geometry
16-XX Associative rings and algebras [For the commutative case, see 13-XX]
- 16G20 Representations of quivers and partially ordered sets
- 16N40 Nil and nilpotent radicals, sets, ideals, rings
- 16U20 Ore rings, multiplicative sets, Ore localization
18-XX Category theory; homological algebra [For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology]
- 18B05 Category of sets, characterizations [See also 03-XX]
- 18G30 Simplicial sets, simplicial objects (in a category) [See also 55U10]
20-XX Group theory and generalizations
- 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) [For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05]
- 20M30 Representation of semigroups; actions of semigroups on sets
- 20N02 Sets with a single binary operation (groupoids)
26-XX Real functions [See also 54C30]
28-XX Measure and integration [For analysis on manifolds, see 58-XX]
- 28A05 Classes of sets (Borel fields,
 -rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
- 28A10 Real- or complex-valued set functions
- 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24]
- 28A25 Integration with respect to measures and other set functions
- 28Bxx Set functions, measures and integrals with values in abstract spaces
- 28B05 Vector-valued set functions, measures and integrals [See also 46G10]
- 28B10 Group- or semigroup-valued set functions, measures and integrals
- 28B15 Set functions, measures and integrals with values in ordered spaces
- 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 49J53, 54C60, 54C65]
- 28Cxx Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]
- 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
- 28C10 Set functions and measures on topological groups, Haar measures, invariant measures [See also 22Axx, 43A05]
- 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
- 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
- 28E15 Other connections with logic and set theory
30-XX Functions of a complex variable [For analysis on manifolds, see 58-XX]
- 30D40 Cluster sets, prime ends, boundary behavior
32-XX Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12]
- 32A60 Zero sets of holomorphic functions
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
32A10
- 32B10 Germs of analytic sets, local parametrization
- 32B15 Analytic subsets of affine space
- 32B20 Semi-analytic sets and subanalytic sets [See also 14P15]
- 32C07 Real-analytic sets, complex Nash functions [See also 14P15, 14P20]
- 32C25 Analytic subsets and submanifolds
- 32C30 Integration on analytic sets and spaces, currents [For local theory, see 32A25 or 32A27]
- 32U30 Removable sets
[Nouveau code MSC 2000]
35-XX Partial differential equations
- 35A18 Wave front sets
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
35A99
- 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15]
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
- 37B35 Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
54H20, 58F99
- 37D05 Hyperbolic orbits and sets
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
58F09, 58F15
- 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
[Nouveau code MSC 2000]
- 37F50 Small divisors, rotation domains and linearization; Fatou and Julia sets [See also 30D05]
[Nouveau code MSC 2000]
- 37G30 Infinite nonwandering sets arising in bifurcations
[Nouveau code MSC 2000]
- Codes MSC1991 affiliés :
34C23, 58F14
- 37L25 Inertial manifolds and other invariant attracting sets
[Nouveau code MSC 2000]
42-XX Fourier analysis
- 42A65 Completeness of sets of functions
- 42C30 Completeness of sets of functions
43-XX Abstract harmonic analysis [For other analysis on topological and Lie groups, see 22Exx]
- 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]
- 46A55 Convex sets in topological linear spaces; Choquet theory [See also 52A07]
47-XX Operator theory
- 47A25 Spectral sets
- 47H04 Set-valued operators [See also 28B20, 54C60, 58C06]
- 47H09 Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, A-proper mappings, K-set contractions, etc.)
- 47L07 Convex sets and cones of operators [See also 46A55]
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
47D20
49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
- 49J53 Set-valued and variational analysis [See also 26E25, 28B20, 47H04, 54C60, 58C06]
[Nouveau code MSC 2000]
- 49Q20 Variational problems in a geometric measure-theoretic setting
51-XX Geometry [For algebraic geometry, see 14-XX]
- 51E21 Blocking sets, ovals, k-arcs
52-XX Convex and discrete geometry
- 52-99 Convex sets and related geometric topics (not classified at a more specific level)
- 52A05 Convex sets without dimension restrictions
- 52A07 Convex sets in topological vector spaces [See also 46A55]
- 52A10 Convex sets in 2 dimensions (including convex curves) [See also 53A04]
- 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also 53A05, 53C45]
- 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
- 52A22 Random convex sets and integral geometry [See also 53C65, 60D05]
- 52A27 Approximation by convex sets
- 52A30 Variants of convex sets (star-shaped, (m, n)-convex, etc.)
54-XX General topology [For the topology of manifolds of all dimensions, see 57Nxx]
- 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
- 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] [For ultrafilters, see 54D80]
- 54C50 Special sets defined by functions [See also 26A21]
- 54C60 Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
- 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
55-XX Algebraic topology
- 55Q05 Homotopy groups, general; sets of homotopy classes
- 55U10 Simplicial sets and complexes [See also 13F55]
57-XX Manifolds and cell complexes [For complex manifolds, see 32Qxx]
- 57N50 Sn-1
 En, Schoenflies problem
58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]
60-XX Probability theory and stochastic processes [For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX]
- 60D05 Geometric probability, stochastic geometry, random sets [See also 52A22, 53C65]
91-XX Game theory, economics, social and behavioral sciences
- 91A44 Games involving topology or set theory
[Nouveau code MSC 2000]
- Code MSC1991 affilié :
90D44
93-XX Systems theory; control [For optimal control, see 49-XX]
94-XX Information and communication, circuits
- 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also 11H71]
- 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]
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