Formaalsetsetel

Formaalsetsetel is a term used in some theoretical discussions of formal structures. It denotes a formal subset of a given set, defined by a predicate or rule expressed in formal notation. The concept emphasizes that the selection criterion is specified independently of informal interpretation, relying instead on a precise, checkable specification.

In formal language theory and set theory, a formal subset is the collection of all elements of a base set that satisfy the predicate. When the predicate is computable, membership in the formaalsetsetel can be determined algorithmically, and the subset is amenable to standard constructions such as union, intersection, and complement (subject to the properties of the base set).

Examples include the set of even-length strings over the alphabet {0,1}, defined by a predicate that checks the string length, and the set of prime numbers represented in decimal notation, defined by a numeric predicate. In automata terms, a formal subset corresponds to the language recognized by a deterministic or nondeterministic automaton.

Formaalsetsetel serves as a pedagogical device to distinguish between informal descriptions of a group of objects and a rigorously defined collection formed by applying a rule. It is closely related to the ideas of formal languages, definable sets, and predicate logic.

See also: formal language, subset, predicate, decidability, automaton.