Editing Kleene's recursion theorem (section)

=== Comparison to the second recursion theorem ===
Compared to the second recursion theorem, the first recursion theorem produces a stronger conclusion but only when narrower hypotheses are satisfied. Rogers uses the term '''weak recursion theorem''' for the first recursion theorem and '''strong recursion theorem''' for the second recursion theorem.{{sfn|Rogers|1967}}

One difference between the first and second recursion theorems is that the fixed points obtained by the first recursion theorem are guaranteed to be least fixed points, while those obtained from the second recursion theorem may not be least fixed points.

A second difference is that the first recursion theorem only applies to systems of equations that can be recast as recursive operators. This restriction is similar to the restriction to continuous operators in the [[Kleene fixed-point theorem]] of [[order theory]]. The second recursion theorem can be applied to any total recursive function.