expressible

Expressible means capable of being expressed or stated in some form. In mathematics and logic, it describes objects, properties, or functions that can be described by a formula or expression in a specified formal language or within a particular structure.

In logic and model theory, an object or a set is expressible (often called definable) in a structure if there exists a formula in the language of that structure such that the elements satisfying the formula are exactly the members of the object. Example: in the real field, the set of nonnegative numbers is expressible as {x : x ≥ 0}, and the set of perfect squares is expressible by ∃y (x = y^2). The precise meaning depends on the chosen language and parameters.

In analysis and algebra, a function or expression is expressible in closed form when it can be written using a finite combination of constants, variables, exponentials, logarithms, roots, and other standard operations. Not every function admits a closed-form expression, and some require infinite series or special functions.

In computer science and linguistics, expressibility also refers to the capacity of a programming language or grammatical system to represent ideas, computations, or structures. The notion highlights the expressive power or limitations of a formal system, influencing how readily problems can be formulated or solved within that framework.

See also: definability, expressivity, closed form, definable set, first-order logic.