On bases of closed classes of vector functions of many-valued logic
Diskretnaya Matematika, Tome 28 (2016) no. 2, pp. 127-132.

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

We consider the functional system of vector functions of many-valued logic with the naturally defined operation of superposition and construct examples of closed classes of special type without a basis and with a countable basis.
Keywords: vector function of many-valued logic, superposition, basis.
@article{DM_2016_28_2_a11,
     author = {V. A. Taimanov},
     title = {On bases of closed classes of vector functions of many-valued logic},
     journal = {Diskretnaya Matematika},
     pages = {127--132},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_2_a11/}
}
TY  - JOUR
AU  - V. A. Taimanov
TI  - On bases of closed classes of vector functions of many-valued logic
JO  - Diskretnaya Matematika
PY  - 2016
SP  - 127
EP  - 132
VL  - 28
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2016_28_2_a11/
LA  - ru
ID  - DM_2016_28_2_a11
ER  - 
%0 Journal Article
%A V. A. Taimanov
%T On bases of closed classes of vector functions of many-valued logic
%J Diskretnaya Matematika
%D 2016
%P 127-132
%V 28
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2016_28_2_a11/
%G ru
%F DM_2016_28_2_a11
V. A. Taimanov. On bases of closed classes of vector functions of many-valued logic. Diskretnaya Matematika, Tome 28 (2016) no. 2, pp. 127-132. http://geodesic.mathdoc.fr/item/DM_2016_28_2_a11/

[1] Yablonskii S.V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 2003, 484 pp. | MR

[2] Malcev I., “Graduated products of Post algebras”, Note on multiple-valued logic, 18:13 (1995), 1–4

[3] Malcev I., “Coordinated products of iterative algebras”, Proc. VIII Int. Conf. on Logic and Computer Science, Novi Sad, Yugoslavia, 1997, 1–2

[4] Marchenkov S.S., “O polnote v sisteme $P_3 \times P_3$”, Diskretnaya matematika, 4:1 (1992), 126–145 | MR | Zbl

[5] Marchenkov S.S., “O klassakh Slupetskogo v sistemakh $P_k \times \dots \times P_l$”, Diskretnaya matematika, 4:3 (1992), 135–148 ; Marchenkov S. S., “On the Slupecki classes in the systems $P_k \times \dots \times P_l$”, Discrete Math. Appl., 3:2 (1993), 147–160 | MR | Zbl | DOI

[6] Marchenkov S.S., “O predpolnykh klassakh v dekartovykh proizvedeniyakh $P_2$ i $P_3$”, Diskretnaya matematika, 6:2 (1994), 21–42 | MR | Zbl

[7] Romov B.A., “Algoritm resheniya problemy polnoty v klasse vektornykh funktsionalnykh sistem”, Matem. modeli slozhnykh sistem, IK AN USSR, Kiev, 1973, 151–155

[8] Romov B.A., “O reshetke podalgebr pryamykh proizvedenii algebr Posta konechnoi stepeni”, Matematicheskie modeli slozhnykh sistem., IK AN USSR, Kiev, 1973, 156–168

[9] Romov B.A., “O polnote na kvadrate funktsii algebry logiki i v sistemakh $P_k \times P_l$”, Kibernetika, 4 (1987), 9–14 | MR | Zbl

[10] Romov B.A., “Ob odnoi serii maksimalnykh podalgebr pryamykh proizvedenii algebr konechnoznachnykh logik”, Kibernetika, 1989, no. 3, 11–16 ; Romov B. A., “A series of maximum subalgebras of direct products of algebras of finite-valued logics”, Cybernetics and Systems Analysis, 25:3, 300–306 | MR | Zbl

[11] Romov B.A., “O funktsionalnoi polnote v sisteme $P_2 \times P_k$”, Kibernetika, 1 (1991), 1–8 ; Romov B. A., “Functional completeness in $P_2 \times P_k$”, Cybernetics and Systems Analysis, 27:1, 1–10 | MR | Zbl

[12] Romov B.A., “The completness problem on the product of algebras of finite-valued logic”, Int. Symp. Multiple-Valued Logic, Boston, USA, 1994, 184–186

[13] Taimanov V.A., “O dekartovykh stepenyakh $P_2$”, Dokl. AN SSSR, 270:6 (1983), 1327–1330 | MR | Zbl

[14] Taimanov V.A., “O bazisakh zamknutykh klassov v $P_k \times P_m$”, Tez. dokl. VIII Vsesoyuzn. konf. “Problemy teoreticheskoi kibernetiki”, Irkutsk, 1985, 188–189

[15] 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

[16] Yablonskii S.V., Gavrilov G.P., Kudryavtsev V.B., Funktsii algebry logiki i klassy Posta, Nauka, Moskva, 1966, 120 pp. | MR

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

[18] Post E.L., Two-valued iterative systems of mathematical logic, Princeton Univ. Press, Princeton, 1941, 122 pp. | MR | Zbl