Fashion or shape (a three-dimensional figure or object) in a malleable material such as clay or wax.
In mathematics, model theory is the study of (classes of) mathematical structures (e.g. groups, fields, graphs, universes of set theory) using tools from mathematical logic. It has close ties to abstract algebra, particularly universal algebra.
Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal languages. If a model for a language moreover satisfies a particular sentence or theory (set of sentences satisfying special conditions), it is called a model of the sentence or theory.
This article focuses on finitary first order model theory of infinite structures. Finite model theory, which concentrates on finite structures, 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.
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