Geodesic
Countable Ideals in a Semi-Lattice of the $\mathbf{D}_e$ Enumeration Degrees
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 4, pp. 59-66

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In the article we have proved that any countable ideal in the semi-lattice of the $\mathbf{D}_e$ is the intersection of two principal ideals generated by quasi-minimal covers for this ideal.
Keywords: ideals, principal ideal of enumeration degrees, enumeration reducible, quasi-minimal enumeration degree. 
@article{MAIS_2012_19_4_a4,
     author = {V. V. Tikhov},
     title = {Countable {Ideals} in a {Semi-Lattice}  of the $\mathbf{D}_e$ {Enumeration} {Degrees}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {59--66},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_4_a4/}
}
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V. V. Tikhov. Countable Ideals in a Semi-Lattice  of the $\mathbf{D}_e$ Enumeration Degrees. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 4, pp. 59-66. http://geodesic.mathdoc.fr/item/MAIS_2012_19_4_a4/