fogalmazhatók

Fogalmazhatók is a Hungarian term used in logic and mathematics to describe entities that can be expressed by a formal formula within a given language. In this usage, a set, relation, or property is said to be fogalmazható in a language L if there exists a formula in L whose interpretation matches the entity in a chosen structure M.

Formally, let M be a structure for a language L. A subset A of the domain of M is fogalmazható in L (in M) if there exists an L-formula φ such that for every element a in M, a ∈ A if and only if M ⊨ φ[a]. Similarly, an n-ary relation R ⊆ M^n is fogalmazható if there is φ with M ⊨ φ[a1,...,an] exactly when (a1,...,an) ∈ R.

Examples help illustrate the idea. In the language of arithmetic with + and ×, the property of being even is fogalmazható by ∃y (x = (1+1)·y). The set of squares is definable by ∃y (x = y^2). In graph theory, with a binary edge relation E, the formula ∃x E(x,x) expresses that the graph has a loop; the broader property of connectedness, however, is not first-order definable in general.

Notes: the term is closely related to definability, though some contexts distinguish scope or perspective (definability across models versus existence of a single defining formula in a given language). See also definability and first-order logic.