Editing Kleene's recursion theorem (section)

=== Fixed-point-free functions ===
A function <math>F</math> such that <math> \varphi_e \not \simeq \varphi_{F(e)}</math> for all <math>e</math> is called '''fixed-point free'''.  The fixed-point theorem shows that no total computable function is fixed-point free, but there are many non-computable fixed-point-free functions. '''Arslanov's completeness criterion''' states that the only [[recursively enumerable]] [[Turing degree]] that computes a fixed-point-free function is '''0&prime;''', the degree of the [[halting problem]].{{r|Soare1987_88}}