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

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.