The noneffectivity of Arslanov’s completeness criterion and related theorems
Sebastiaan A. Terwijn · Archive for Mathematical Logic · 2020
Abstract We discuss the (non)effectivity of Arslanov’s completeness criterion. In particular, we show that a parameterized version, similar to the recursion theorem with parameters, fails. We also discuss the effectivity of another extension of the recursion theorem, namely Visser’s ADN theorem, as well as that of a joint generalization of the ADN theorem and Arslanov’s completeness criterion.