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Mathematics Subject Classification – MSC2020
03XX
Mathematical logic and foundations
112374
03Cxx
Model theory
14486
03C05
Equational classes, universal algebra in model theory
[See also
08Axx
,
08Bxx
,
18C05
]
976
03C07
Basic properties of firstorder languages and structures
579
03C10
Quantifier elimination, model completeness and related topics
881
03C13
Model theory of finite structures
[See also
68Q15
,
68Q19
]
883
03C15
Model theory of denumerable and separable structures
533
03C20
Ultraproducts and related constructions
569
03C25
Modeltheoretic forcing
198
03C30
Other model constructions
329
03C35
Categoricity and completeness of theories
1174
03C40
Interpolation, preservation, definability
779
03C45
Classification theory, stability and related concepts in model theory
[See also
03C48
]
1773
03C48
Abstract elementary classes and related topics
[See also
03C45
]
101
03C50
Models with special properties (saturated, rigid, etc.)
615
03C52
Properties of classes of models
401
03C55
Settheoretic model theory
292
03C57
Computable structure theory, computable model theory
[See also
03D45
]
958
03C60
Modeltheoretic algebra
[See also
08C10
,
12Lxx
,
13L05
]
3020
03C62
Models of arithmetic and set theory
[See also
03Hxx
]
718
03C64
Model theory of ordered structures; ominimality
794
03C65
Models of other mathematical theories
465
03C66
Continuous model theory, model theory of metric structures
5
03C68
Other classical firstorder model theory
633
03C70
Logic on admissible sets
136
03C75
Other infinitary logic
616
03C80
Logic with extra quantifiers and operators
[See also
03B42
,
03B44
,
03B45
,
03B48
]
816
03C85
Second and higherorder model theory
230
03C90
Nonclassical models (Booleanvalued, sheaf, etc.)
431
03C95
Abstract model theory
297
03C98
Applications of model theory
[See also
03C60
]
319
03C99
None of the above, but in this section
785
Overview
00
General and overarching topics; collections
01
History and biography
03
Mathematical logic and foundations
05
Combinatorics
06
Order, lattices, ordered algebraic structures
08
General algebraic systems
11
Number theory
12
Field theory and polynomials
13
Commutative algebra
14
Algebraic geometry
15
Linear and multilinear algebra; matrix theory
16
Associative rings and algebras
17
Nonassociative rings and algebras
18
Category theory; homological algebra
19
\(K\)theory
20
Group theory and generalizations
22
Topological groups, Lie groups
26
Real functions
28
Measure and integration
30
Functions of a complex variable
31
Potential theory
32
Several complex variables and analytic spaces
33
Special functions
34
Ordinary differential equations
35
Partial differential equations
37
Dynamical systems and ergodic theory
39
Difference and functional equations
40
Sequences, series, summability
41
Approximations and expansions
42
Harmonic analysis on Euclidean spaces
43
Abstract harmonic analysis
44
Integral transforms, operational calculus
45
Integral equations
46
Functional analysis
47
Operator theory
49
Calculus of variations and optimal control; optimization
51
Geometry
52
Convex and discrete geometry
53
Differential geometry
54
General topology
55
Algebraic topology
57
Manifolds and cell complexes
58
Global analysis, analysis on manifolds
60
Probability theory and stochastic processes
62
Statistics
65
Numerical analysis
68
Computer science
70
Mechanics of particles and systems
74
Mechanics of deformable solids
76
Fluid mechanics
78
Optics, electromagnetic theory
80
Classical thermodynamics, heat transfer
81
Quantum theory
82
Statistical mechanics, structure of matter
83
Relativity and gravitational theory
85
Astronomy and astrophysics
86
Geophysics
90
Operations research, mathematical programming
91
Game theory, economics, finance, and other social and behavioral sciences
92
Biology and other natural sciences
93
Systems theory; control
94
Information and communication theory, circuits
97
Mathematics education
W3C
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