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: \(A ≤_m B ∃ f ∈ recursive, ∀ x: x ∈ A f(x) ∈ B\). Turing degree: \(A ≡_T B A ≤_T B B ≤_T A\). The c.e. many-one degrees form an upper semilattice with least element \(0_m\) (decidable sets) and maximal c.e. degree \(0'_m\) (halting problem). The new theorem: \(∃ d ∈ c.e. many-one degrees, d ≠ 0_m\), such that no finite-one degree \(f ≤_m d\) is minimal below \(d\). | 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 \(≤_m\) mirror Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com