Computability, Logic, AI Algorithms Open access Peer reviewed

A diamond embedding in the computably enumerable quasi degrees

Kai Jun Khoo, Keng Meng Ng

Archive for Mathematical Logic | Oct 29, 2026

Abstract

Abstract We investigate the relationship between $$\le _{Q}$$ ≤ Q and $$\le _{T}$$ ≤ T on the computably enumerable sets by asking what kind of lattices can be embedded in the computably enumerable Q degrees, with elements of the lattice in the same Turing degree. We will use a pinball machine to show that the diamond lattice can be embedded in the computably enumerable Q degrees, with all elements of the lattice in the same Turing degree.

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Authors

Researchers on this paper

Kai Jun Khoo

first | Victoria University of Wellington

Keng Meng Ng

last | Nanyang Technological University | ORCID 0000-0002-7113-0596

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Advanced Topology and Set Theory Latest Computability, Logic, AI Algorithms research semigroups and automata theory

Citation

BibTeX

@article{Khoo2026diamond,
  title = {A diamond embedding in the computably enumerable quasi degrees},
  author = {Kai Jun Khoo and Keng Meng Ng},
  journal = {Archive for Mathematical Logic},
  year = {2026},
  doi = {10.1007/s00153-026-01037-z},
  url = {https://doi.org/10.1007/s00153-026-01037-z}
}

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