\texorpdfstring{$D$}{D}-maximal many-one degrees contain least finite-one degrees

TL;DR

This paper proves that every nonrecursive D-maximal many-one degree containing a D-maximal set also contains a least finite-one degree, using known results and a new duplicate-cover method.

Contribution

It establishes the existence of least finite-one degrees in all nonrecursive D-maximal many-one degrees with a novel proof technique.

Findings

Nonrecursive D-maximal many-one degrees contain least finite-one degrees.

Develops a duplicate-cover method for classifying D-maximal types.

Handles simple cases with known results and introduces new methods for complex cases.

Abstract

Richter, Stephan, and Zhang asked whether every nonrecursive many-one degree contains a least finite-one degree. We prove this for every nonrecursive \ce\ many-one degree containing a $D$-maximal set. The proof handles the simple cases via known results and develops a duplicate-cover method for the remaining $D$-maximal types in the classification of Cholak, Gerdes, and Lange.