Finite final segments of the d.c.e. Turing degrees

2024/03/07 by Steffen Lempp, Lempp, Steffen, Yiqun Liu +9
Computer Science · #03D28 #Coding theory and cryptography #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2403.04254

openalex publication_date 2024/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every finite distributive lattice is isomorphic to a final segment of the d.c.e. Turing degrees (i.e., the degrees of differences of computably enumerable sets). As a corollary, we are able to infer the undecidability of the EAE-theory of the d.c.e. degrees in the language of partial ordering.

Related

• Realizing Computably Enumerable Degrees in Separating Classes
• Bi-Isolated d.c.e. Degrees and Σ₁ Induction
• Lattice initial segments of the Turing degrees
• α degrees as an automorphism base for the α-enumeration degrees
• Computably enumerable partial orders