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High Quality Content by WIKIPEDIA articles! In model theory and related areas of mathematics, a type is a set of first-order formulas in a language L with free variables x_1,x_2,ldots,x_n which are true of a sequence of elements of an L-structure mathcal{A}. Loosely speaking, types describe possible elements of a mathematical structure. Depending on the context, types can be complete or partial and they may use a fixed set of constants from the structure mathcal{A}. The question of which types represent actual elements of mathcal{A} leads to the ideas of saturated models and omitting types.