Generalizations of the Recursion Theorem

TL;DR

This paper explores advanced generalizations of the recursion theorem, specifically Visser's ADN theorem and Arslanov's completeness criterion, and establishes a unified generalization of these foundational results.

Contribution

It introduces a joint generalization of Visser's ADN theorem and Arslanov's completeness criterion, expanding the theoretical framework of recursion theorems.

Findings

Unified generalization of the two theorems

Enhanced understanding of recursion theorem extensions

Potential implications for computability theory

Abstract

We consider two generalizations of the recursion theorem, namely Visser's ADN theorem and Arslanov's completeness criterion, and we prove a joint generalization of these theorems.