Geodesic
Rogers Semilattices of Finite Partially Ordered Sets
Algebra i logika, Tome 45 (2006) no. 1, pp. 44-84.

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It is proved that the principal sublattice of a Rogers semilattice of a finite partially ordered set is definable. For this goal to be met, we present a generalization of the Denisov theorem concerning extensions of embeddings of Lachlan semilattices to ideals of Rogers semilattices.
Keywords: Rogers semilattice, Lachlan semilattice, definability. 
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Yu. L. Ershov. Rogers Semilattices of Finite Partially Ordered Sets. Algebra i logika, Tome 45 (2006) no. 1, pp. 44-84. http://geodesic.mathdoc.fr/item/AL_2006_45_1_a3/

[1] A. H. Lachlan “Recursively enumerable many-one degrees”, Algebra i logika,, 11:3 (1972), 326–358 | MR | Zbl

[2] Yu. L. Ershov, I. A. Lavrov, “Verkhnyaya polureshetka $L(\mathfrak{S})$”, Algebra i logika, 12:2 (1973), 167–189 | MR | Zbl

[3] Yu. L. Ershov, “Neobkhodimye usloviya izomorfizma polureshetok Rodzhersa konechnykh chastichno uporyadochennykh mnozhestv”, Algebra i logika, 42:4 (2003), 413–421 | MR | Zbl

[4] S. D. Denisov, “Stroenie verkhnei polureshetki rekursivno-perechislimykh $m$-stepenei i smezhnye voprosy. I”, Algebra i logika, 17:6 (1978), 643–683 | MR | Zbl

[5] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977 | MR