In mathematics, model theory is the study of (classes of) mathematical structures such as groups, fields, graphs or even models of set theory using tools from mathematical logic. Model theory has close ties to algebra and universal algebra.
This article focuses on finitary first order model theory of infinite structures. The model theoretic study of finite structures (for which see finite model theory) diverges significantly from the study of infinite structures in both the problems studied and the techniques used. Model theory in higher-order logics or infinitary logics is hampered by the fact that completeness does not in general hold for these logics. However, a great deal of study has also been done in such languages.
Reference:
http://en.wikipedia.org/wiki/Model_theory
