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

Voir la notice de l'article provenant de la source Math-Net.Ru

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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     author = {Yu. L. Ershov},
     title = {Rogers {Semilattices} of {Finite} {Partially} {Ordered} {Sets}},
     journal = {Algebra i logika},
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     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_1_a3/}
}
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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/