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We investigate the relationship between ≤ Q ≤ Q and ≤ 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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Khoo et al. (2026) studied this question.
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