Type (model theory)

Concept in model theory

In model theory and related areas of mathematics, a type is an object that describes how a (real or possible) element or finite collection of elements in a mathematical structure might behave. More precisely, it is a set of first-order formulas in a language L with free variables x1, x2,..., xn that are true of a set of n-tuples of an L-structure M {\displaystyle {\mathcal {M}}} . Depending on the context, types can be complete or partial and they may use a fixed set of constants, A, from the structure M {\displaystyle {\mathcal {M}}} .

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