Geodesic
Sublattices and Initial Segments of the Degrees of Unsolvability
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 569-581

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In this paper we shall prove that every finite lattice is isomorphic to a sublattice of the degrees of unsolvability, and that every one of a certain class of finite lattices is isomorphic to an initial segment of degrees. Acknowledgment. I am grateful to Ralph McKenzie for his assistance in matters of lattice theory. 1. Representation of lattices. The equivalence lattice of the set S consists of all equivalence relations on S, ordered by setting θ ≦ θ’ if for all a and b in S, a θ b ⇒ a θ’ b. The least upper bound and greatest lower bound in are given by the ⋃ and ⋂ operations: 
Thomason, S. K. Sublattices and Initial Segments of the Degrees of Unsolvability. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 569-581. doi: 10.4153/CJM-1970-064-7
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