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

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

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/}
}
TY  - JOUR
AU  - A. A. Bulatov
TI  - Abstract properties of a class of intervals of lattices of closed classes
JO  - Diskretnaya Matematika
PY  - 2000
SP  - 95
EP  - 113
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2000_12_3_a6/
LA  - ru
ID  - DM_2000_12_3_a6
ER  - 
%0 Journal Article
%A A. A. Bulatov
%T Abstract properties of a class of intervals of lattices of closed classes
%J Diskretnaya Matematika
%D 2000
%P 95-113
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2000_12_3_a6/
%G ru
%F DM_2000_12_3_a6
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/

[1] Post E., “Two-valued Iterative Systems of Mathematical Logic”, Ann. Math. Stud., 5 (1941), Princeton Univ. Press, Princeton | MR

[2] Bulatov A. A., “Konechnye podreshetki v reshetke klonov”, Algebra i logika, 33:5 (1994), 514–549 | MR | Zbl

[3] Bulatov A. A., “Tozhdestva v reshetkakh zamknutykh klassov”, Diskretnaya matematika, 4:4 (1992), 140–148 | MR | Zbl

[4] Bulatov A. A., “Podreshetki reshetki klonov funktsii na trekhelementnom mnozhestve. I”, Algebra i logika, 38:1 (1999), 3–23 | MR | Zbl

[5] Grettser G., Obschaya teoriya reshetok, Mir, Moskva, 1982 | MR

[6] Yablonskii S. V., “Funktsionalnye postroeniya v $k$-znachnoi logike”, Trudy Matem. in-ta im. V. A. Steklova, 51, 1958, 5–142 | Zbl

[7] Pöschel R., Kalužnin L. A., Funktionen-und Relationenalgebren. Ein Kapitel der diskreten Mathematik VEB DVW, Berlin, 1979 | MR

[8] Yanov Yu. I., Muchnik A. A., “O suschestvovanii $k$-znachnykh zamknutykh klassov, ne imeyuschikh konechnogo bazisa”, Dokl. AN SSSR, 127:1 (1959), 44–46 | Zbl

[9] Haddad L., Rosenberg I. G., “Un intervalle Booléen de clones sur un univers fini”, Ann. Sci. Math. Québec, 12:2 (1988), 211–231 | MR | Zbl

[10] Krokhin A. A., “Monoidalnye intervaly v reshetkakh klonov”, Algebra i logika, 34:3 (1995), 288–310 | MR | Zbl

[11] Bodnarchuk V. G., Kaluzhnin L. A., Kotov V. N., Romov B. A., “Teoriya Galua dlya algebr Posta. I, II”, Kibernetika, 3 (1969), 1–10 ; 5, 1–9 | Zbl