# recursive set

**recursive set** A subset *A* of a set *B* is said to be recursive, relative to *B*, if there is an algorithm or effective procedure that, given an element *b* in *B*, will output “yes” if *b* is an element of *A* and “no” if *b* is not an element of *A*. The set *A* is thus also said to be *decidable* or *computable*.

Strictly speaking the sets *A* and *B* should be sets of natural numbers, and the algorithm is a definition of the total recursive function that is the characteristic function of *A* in *B*. The concept and terminology is transferred to other data sets using a Gödel numbering.

Post's theorem says that a set *A* is recursive iff *A* and *B*–*A* are recursively enumerable.

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