## undecidable

Adjective

(*not comparable*)

- (mathematics, computing theory) Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
- (mathematics) (
*of a WFF*) logically independent from the axioms of a given theory; i.e., that it can*never*be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (*Note:*this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)