definíveis

Definíveis is the plural form of definível, an adjective in Portuguese meaning capable of being defined. The term is used across areas such as logic, mathematics, philosophy, and linguistics to indicate that something can be precisely described or specified within a given framework.

In logic and mathematics, definibilidade refers to the ability to specify objects or sets by a formula. A subset of a structure M^n is definable in M if there exists a first-order formula φ(x1, ..., xn) such that S = { (a1, ..., an) in M^n : M satisfies φ(a1, ..., an) }. When parameters from M are allowed, the subset is definable with parameters; without them, it is definable without parameters. A single element a in M is definable (over a substructure) if there is a formula whose interpretation in M yields exactly a. Definability is central to model theory, influencing how structures are analyzed and compared.

Examples arise in familiar settings: in the real field, semialgebraic sets are definable by polynomial equations and inequalities; in the ring of integers, certain arithmetic sets can be defined using first-order formulas. The notion extends to functions and relations, not only sets.

Definíveis also appears in broader contexts. In philosophy or linguistics, it can describe entities or descriptions that can be explicitly defined or specified. In computer science and formal specification, definability concerns whether a property or behavior can be expressed in a given specification language.

See also: definability, definable set, definable function, first-order logic, model theory, semialgebraic sets.