Geodesic
Abstract properties of a class of intervals of lattices of closed classes
Diskretnaya Matematika, Tome 12 (2000) no. 3, pp. 95-113

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The lattice $\mathcal L_k$ of closed classes that contain all projections (that is, the lattice of clones) on a $k$-element set is considered. It is proved that for any $k\geq 2$ the countable direct degree of $\mathcal L_k$ is isomorphic to an interval in $\mathcal L_{k+3}$. In particular, hence it follows that the class of all sublattices (intervals) of the lattice of clones is closed under countable direct degrees. 
@article{DM_2000_12_3_a6,
     author = {A. A. Bulatov},
     title = {Abstract properties of a class of intervals of lattices of closed classes},
     journal = {Diskretnaya Matematika},
     pages = {95--113},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2000_12_3_a6/}
}
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A. A. Bulatov. Abstract properties of a class of intervals of lattices of closed classes. Diskretnaya Matematika, Tome 12 (2000) no. 3, pp. 95-113. http://geodesic.mathdoc.fr/item/DM_2000_12_3_a6/