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/

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