Definierbar

Definierbar is a German adjective meaning definable or capable of being defined. It is formed from the verb definieren (to define) with the suffix -bar, which signals that something can be described or characterized by a definition. In German-language mathematics, logic and philosophy, definierbar is used to describe objects whose properties or existence can be captured by a definition.

In mathematics and logic, definierbarkeit (definability) is typically relative to a formal language and a structure. A set, relation or function is definierbar in a structure M if there exists a formula in the language of M such that the set consists exactly of those elements satisfying the formula. Definability can be with parameters from M or parameter-free; the latter is sometimes called definierbar ohne Parameter. For example, in the language of ordered fields, the interval (0, 1) is definierbar by the formula 0 < x and x < 1. With parameters, a subset specified by x = a for some a in M is definable.

Definierbar is used across areas such as model theory, algebraic geometry and computer science, wherever precise description by a formula is relevant. Related terms include Definierbarkeit (definability) and definierbare Menge (definable set). The concept underpins discussions of what can be described, characterized, or computed within a given formal framework.

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