# Decidable predicate

An $n$-place predicate $P$ given on a certain set of constructive objects (for example, natural numbers) $M$ for which there exists an algorithm which enables one to find the value (T or F) of $P$ on any $n$-tuple $a_1,\ldots,a_n$ of elements in $M$. In other words, a predicate is decidable if, regarded as an $n$-place function on $M$ with values in the set $\{\text T,\text F\}$, it is a computable function.

When the concept of a recursive function or some equivalent concept is used as a mathematical refinement of the concept of computability, then the term "recursive predicate" is usually employed instead of "decidable predicate" .

#### Comments

So, $P$ is a decidable predicate if the set of $n$-tuples on which $P$ takes the value T (true) is a decidable set.

**How to Cite This Entry:**

Decidable predicate.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Decidable_predicate&oldid=34430