03C05 Equational classes, universal algebra [See also 08Axx, 08Bxx, 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