Editing Decidability (logic) (section)

== Relationship to computability ==

As with the concept of a [[decidable set]], the definition of a decidable theory or logical system can be given either in terms of ''[[effective method]]s'' or in terms of ''[[computable function]]s''. These are generally considered equivalent per [[Church's thesis]]. Indeed, the proof that a logical system or theory is undecidable will use the formal definition of computability to show that an appropriate set is not a decidable set, and then invoke Church's thesis to show that the theory or logical system is not decidable by any effective method (Enderton 2001, pp.&nbsp;206''ff.'').