Recursive predicate

A predicate $ P( x _ {1} \dots x _ {n} ) $ defined on the natural numbers, such that the function $ f $ defined on the natural numbers by the condition

$$ f( x _ {1} \dots x _ {n} ) = \left \{ \begin{array}{ll} 1 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is true }, \\ 0 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is false } , \\ \end{array} \right .$$

is a recursive function.