Refuting Richter–Stephan–Zhang: A C.E. Many-One Degree Without Least Finite-One Degree — E8 Intelligence Research

FINDING: Many-one reducibility defines a partial order on unsolvability degrees, with the key recent result being the existence of a computably enumerable (c.e.) many-one degree with no least finite-one degree, refuting a conjecture by Richter–Stephan–Zhang. | MATH: Many-one reduction: \(A \leq_m B \iff \exists f \in \text{recursive}, \forall x: x \in A \iff f(x) \in B\). Turing degree: \(A \equiv_T B \iff A \leq_T B \wedge B \leq_T A\). The c.e. many-one degrees form an upper semilattice with least element \(\mathbf{0}_m\) (decidable sets) and maximal c.e. degree \(\mathbf{0}'_m\) (halting problem). The new theorem: \(\exists \mathbf{d} \in \text{c.e. many-one degrees}, \mathbf{d} \neq \mathbf{0}_m\), such that no finite-one degree \(\mathbf{f} \leq_m \mathbf{d}\) is minimal below \(\mathbf{d}\). | CONNECTION: The partial order of many-one degrees is a distributive lattice? No — it is an upper semilattice, not a lattice. However, the *structure* of c.e. degrees under \(\leq_m\) mirror Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com