meghatározhatóke

Meghatározhatóke is a term used in Hungarian discussions of logic and philosophy to denote the property of being definable or determinable within a given formal system. The notion concerns whether a particular object, relation, or set can be described unambiguously by a finite description or by a formula in a specified language or theory. In practice, meghatározhatóke is often discussed as a question of definability: can the members of a subset be exactly characterized by a formula that holds only for those members in every model of the theory?

In model theory, a subset S of a structure M is meghatározhatóke in M if there exists a formula φ(x) of the language L such that S = { a in M : M ⊨ φ(a) }. If the definition is allowed to use parameters from M, the subset is definable with parameters; without parameters it is definable without them. The term thus overlaps with standard terminology definability, though it is used here to emphasize the question form in Hungarian discourse.

Different but related notions include decidability and computability. Definability concerns the existence of a description in the language that singles out the object, while decidability asks whether a given statement or problem can be resolved by an algorithm in a finite amount of time within a theory. An object can be meghatározhatóke yet undecidable in a given formal system, illustrating the separation between definability and algorithmic solvability.

Examples in mathematics illustrate the idea, but the status of definability depends on the chosen language; in finite structures, the expressive power often suffices to define many natural subsets. The concept connects to broader discussions of descriptive set theory and the expressive limits of logical languages.