Geodesic
Definable functions of universal algebras and definable equivalence between algebras
Algebra i logika, Tome 53 (2014) no. 2, pp. 256-270.

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

Research into universal algebras (for different classifications included) is generally confined to working with termal (or polynomial) functions of these algebras. Attempts to go beyond the range of the functions mentioned while staying within the frames of functions naturally definable on the algebras under consideration led the author to the idea of studying conditional termal functions (and their different generalizations such as positively, elementarily conditional termal, implicit, and abstract functions). As a continuation of studies in naturally definable functions on universal algebras, we propose to consider $L$-definable functions, where $L$ is some logical language. This most general approach turns out to be connected with a scheme for defining conditional termal functions and their generalizations, as well as with various derivative structures of universal algebras. Here we present $L$-definable functions on universal algebras and outline their basic properties. On this basis, also, we introduce the notion of $L$-definably equivalent algebras, which is a generalization of the concept of being rationally equivalent for algebras.
Keywords: universal algebra, $L$-definable function on universal algebra, $L$-definably equivalent algebras. 
@article{AL_2014_53_2_a6,
     author = {A. G. Pinus},
     title = {Definable functions of universal algebras and definable equivalence between algebras},
     journal = {Algebra i logika},
     pages = {256--270},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2014_53_2_a6/}
}
TY  - JOUR
AU  - A. G. Pinus
TI  - Definable functions of universal algebras and definable equivalence between algebras
JO  - Algebra i logika
PY  - 2014
SP  - 256
EP  - 270
VL  - 53
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2014_53_2_a6/
LA  - ru
ID  - AL_2014_53_2_a6
ER  - 
%0 Journal Article
%A A. G. Pinus
%T Definable functions of universal algebras and definable equivalence between algebras
%J Algebra i logika
%D 2014
%P 256-270
%V 53
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2014_53_2_a6/
%G ru
%F AL_2014_53_2_a6
A. G. Pinus. Definable functions of universal algebras and definable equivalence between algebras. Algebra i logika, Tome 53 (2014) no. 2, pp. 256-270. http://geodesic.mathdoc.fr/item/AL_2014_53_2_a6/

[1] A. G. Pinus, Uslovnye termy i ikh primenenie v algebre i teorii vychislenii, Izd-vo NGTU, Novosibirsk, 2002

[2] A. G. Pinus, “Uslovnye termy i ikh prilozheniya v algebre i teorii vychislenii”, Uspekhi matem. n., 56:4(340) (2001), 35–72 | DOI | MR | Zbl

[3] A. G. Pinus, “Ratsionalnaya ekvivalentnost algebr, eë ‘klonovye’ obobscheniya i ‘klonovaya kategorichnost’ ”, Sib. matem. zh., 54:3 (2013), 673–688 | MR | Zbl

[4] A. G. Pinus, “Tochechno termalno polnye klony funktsii i reshetki reshetok vsekh podalgebr algebr s fiksirovannym osnovnym mnozhestvom”, Izv. IrGU. Ser. matem., 2012, no. 3, 94–103 | MR | Zbl

[5] A. G. Pinus, “$n$-elementarnaya vlozhimost i $n$-uslovnye termy”, Izv. vuzov. Matem., 1999, no. 1, 36–40 | MR | Zbl

[6] C. Karp, Languages with expressions of infinite length, North-Holland Publ. Co., Amsterdam, 1964 | MR | Zbl

[7] D. Scott, “Logic with denumerably long formulas and finite strings of quantifiers”, The theory of models, eds. J. Addison, L. Henkin, A. Tarski, North-Holland Publ. Co., Amsterdam, 1970, 329–341 | MR

[8] A. G. Pinus, “O klassicheskom Galua-zamykanii dlya universalnykh algebr”, Izv. vuzov. Matem., 2014, no. 2, 47–53

[9] A. I. Maltsev, “Strukturnaya kharakteristika nekotorykh klassov algebr”, Dokl. AN SSSR, 120:1 (1958), 29–32 | Zbl

[10] G. Birkhoff, “Über Gruppen von Automorphismen”, Rev. Unión Mat. Argent., 11 (1946), 155–157 (Spanish) | MR | Zbl

[11] A. G. Pinus, “Ischislenie uslovnykh tozhdestv i uslovno ratsionalnaya ekvivalentnost”, Algebra i logika, 37:4 (1998), 432–459 | MR | Zbl

[12] A. G. Pinus, Proizvodnye struktury universalnykh algebr, Izd-vo NGTU, Novosibirsk, 2007 | Zbl