primitive recursive predicate

primitive recursive predicates are primitive recursive functions whose range is $\text{[math]}$ , 0 and 1 being substitutes for true and false.
[cite:;taken from @computability_davis_1994 chapter 3.5 primitive recursive functions]

the function $\text{[math]}$ is defined as
$\text{[math]}$ $\text{[math]}$ is primitive recursive since
$\text{[math]}$ or we can simply write the recursion equations:
$\text{[math]}$ [cite:;taken from @computability_davis_1994 chapter 3.5 primitive recursive functions]

the predicate is defined as 1 if the values of $\text{[math]}$ and $\text{[math]}$ are the same and 0 otherwise. thus we wish to show that the function
$\text{[math]}$ is primitive recursive. this follows immediately from the equation
$\text{[math]}$ [cite:;taken from @computability_davis_1994 chapter 3.5 primitive recursive functions]

this predicate is simply the primitive recursive function $\text{[math]}$ .
[cite:;taken from @computability_davis_1994 chapter 3.5 primitive recursive functions]

let $\text{[math]}$ be a PRC class. if $\text{[math]}$ are predicates that belong to $\text{[math]}$ , then so are $\text{[math]}$ , and $\text{[math]}$ .
[cite:;taken from @computability_davis_1994 theorem 5.1]

we can write
$\text{[math]}$ or more simply
$\text{[math]}$ [cite:;taken from @computability_davis_1994 chapter 3.5 primitive recursive functions]

let $\text{[math]}$ be a PRC class. let the functions $\text{[math]}$ and the predicate $\text{[math]}$ belong to $\text{[math]}$ . let
$\text{[math]}$ then $\text{[math]}$ belongs to $\text{[math]}$ .
[cite:;taken from @computability_davis_1994 theorem 5.4]

let $\text{[math]}$ be a PRC class, let $\text{[math]}$ -ary functions $\text{[math]}$ and predicates $\text{[math]}$ belong to $\text{[math]}$ , and let
$\text{[math]}$ for all $\text{[math]}$ and all $\text{[math]}$ . if
$\text{[math]}$ then $\text{[math]}$ also belongs to $\text{[math]}$ .
[cite:;taken from @computability_davis_1994 corollary 5.5]

if the predicate $\text{[math]}$ belongs to some PRC class $\text{[math]}$ , then so do the predicates
$\text{[math]}$ this is directly related to unbounded_search_operator.html.
[cite:;taken from @computability_davis_1994 theorem 6.3]

$\text{[math]}$ is the predicate "y is a divisor of $\text{[math]}$ ." for example.
$\text{[math]}$ is true, while
$\text{[math]}$ is false.
the predicate is primitive recursive since
$\text{[math]}$ [cite:;taken from @computability_davis_1994 chapter 3.6 iterated operations and bounded quantifiers]

the predicate " $\text{[math]}$ is a prime" is primitive recursive since
$\text{[math]}$ (a number is a prime if it is greater than 1 and it has no divisors other than 1 and itself.)
[cite:;taken from @computability_davis_1994 chapter 3.6 iterated operations and bounded quantifiers]