Geodesic
Equational closure
Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 117-126.

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

On the base of equation calculus, we define the operator of equational closure. We give examples of equationally complete systems and equationally closed classes. We find the cardinality of the set of equationally precomplete classes and give criteria of equational completeness. We present all equationally closed classes of Boolean functions.This research was supported by the Russian Foundation for Basic Research, grant 03–01–00783. 
@article{DM_2005_17_2_a8,
     author = {S. S. Marchenkov},
     title = {Equational closure},
     journal = {Diskretnaya Matematika},
     pages = {117--126},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2005_17_2_a8/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - Equational closure
JO  - Diskretnaya Matematika
PY  - 2005
SP  - 117
EP  - 126
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2005_17_2_a8/
LA  - ru
ID  - DM_2005_17_2_a8
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T Equational closure
%J Diskretnaya Matematika
%D 2005
%P 117-126
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2005_17_2_a8/
%G ru
%F DM_2005_17_2_a8
S. S. Marchenkov. Equational closure. Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 117-126. http://geodesic.mathdoc.fr/item/DM_2005_17_2_a8/

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

[2] Golunkov Yu. V., “Polnota sistem funktsii v operatornykh algoritmakh, realizuyuschikh funktsii $k$-znachnoi logiki”, Veroyatnostnye metody i kibernetika, 1980, no. 17, 23–34 | MR | Zbl

[3] Danilchenko A. F., “O parametricheskoi vyrazimosti funktsii trekhznachnoi logiki”, Algebra i logika, 16:4 (1977), 397–416 | MR

[4] Klini S. K., Vvedenie v metamatematiku, IL, Moskva, 1957

[5] Kon P., Universalnaya algebra, Mir, Moskva, 1968 | MR

[6] Kuznetsov A. V., “O sredstvakh dlya obnaruzheniya nevyvodimosti i nevyrazimosti”, Logicheskii vyvod, Nauka, Moskva, 1979, 5–33

[7] Marchenkov S. S., “Odnorodnye algebry”, Problemy kibern., 39 (1982), 85–106 | MR | Zbl

[8] Marchenkov S. S., “Klonovaya klassifikatsiya dualno diskriminatornykh algebr s konechnym nositelem”, Matem. zametki, 61:3 (1997), 359–366 | MR | Zbl

[9] Marchenkov S. S., “$S$-klassifikatsiya funktsii mnogoznachnoi logiki”, Diskretnaya matematika, 9:3 (1997), 125–152 | MR | Zbl

[10] Marchenkov S. S., “$A$-klassifikatsiya funktsii mnogoznachnoi logiki”, Dokl. RAN, 366:4 (1999), 455–457 | MR | Zbl

[11] Marchenkov S. S., “O vyrazimosti funktsii mnogoznachnoi logiki v nekotorykh logiko-funktsionalnykh yazykakh”, Diskretnaya matematika, 11:4 (1999), 110–126 | MR | Zbl

[12] Marchenkov S. S., Zamknutye klassy bulevykh funktsii, Fizmatlit, Moskva, 2000 | MR | Zbl

[13] Marchenkov S. S., $S$-klassifikatsiya funktsii trekhznachnoi logiki, Fizmatlit, Moskva, 2001

[14] Marchenkov S. S., Vestnik MGU. Seriya 1. Matematika, mekhanika, 2003, no. 6, 37–39 | MR | Zbl

[15] Nguen Van Khoa, “O strukture samodvoistvennykh zamknutykh klassov trekhznachnoi logiki $P_3$”, Diskretnaya matematika, 4:4 (1992), 82–95 | MR

[16] Nguen Van Khoa, “O semeistvakh zamknutykh klassov $k$-znachnoi logiki, sokhranyaemykh vsemi avtomorfizmami”, Diskretnaya matematika, 1993, no. 4, 87–108 | MR | Zbl

[17] Nguen Van Khoa, “O zamknutykh klassakh $k$-znachnoi logiki, samodvoistvennykh otnositelno tranzitivnykh grupp”, Diskretnaya matematika, 8:1 (1998), 129–156 | MR

[18] Solovev V. D., “Zamknutye klassy v $k$-znachnoi logike s operatsiei razvetvleniya po predikatu”, Diskretnaya matematika, 2:4 (1990), 19–25 | MR

[19] Taimanov V. A., “O funktsionalnykh sistemakh $k$-znachnoi logiki s operatsiyami programmnogo tipa”, Dokl. AN SSSR, 268:6 (1983), 1307–1310 | MR | Zbl

[20] Yablonskii S. V., “Funktsionalnye postroeniya v $k$-znachnoi logike”, Tr. MIAN, 51, 1958, 5–142 | Zbl

[21] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 1986 | MR

[22] Yablonskii S. V., Gavrilov G. P., Kudryavtsev V. B., Funktsii algebry logiki i klassy Posta, Nauka, Moskva, 1966 | MR | Zbl

[23] 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

[24] Barris S., Willard R., “Finitely many primitive positive clones”, Proc. Amer. Math. Soc., 101:3 (1987), 427–430 | DOI | MR

[25] Marczewski E., “Homogeneous operations and homogeneous algebras”, Fund. Math., 56:2 (1964), 81–103 | MR | Zbl

[26] Post E. L., “Introduction to a general theory of elementary propositions”, Amer. J. Math., 43 (1921), 163–185 | DOI | MR | Zbl

[27] Post E. L., The two-valued iterative systems of mathematical logic, Princeton Univ. Press, Princeton, NJ, 1941 | MR | Zbl

[28] Rosenberg I. G., “Über die funktionale Vollständigkeit in den mehrwertigen Logiken”, Rozpravy Českosl. Acad. Věd., Ř. Mat. Přír. Věd., 80:4 (1970), 3–93 | MR