On semilattices and lattices for families of theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 980-985

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

We define and study semilattices and lattices for $E$-closed families of theories. Properties of these semilattices and lattices are investigated. It is shown that lattices for families of theories with the least generating sets are distributive.
Keywords: $E$-operator, combination of theories, family of theories, least generating set, semilattice, lattice.
S. V. Sudoplatov. On semilattices and lattices for families of theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 980-985. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a27/
@article{SEMR_2017_14_a27,
     author = {S. V. Sudoplatov},
     title = {On semilattices and lattices for families of theories},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {980--985},
     year = {2017},
     volume = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a27/}
}
TY  - JOUR
AU  - S. V. Sudoplatov
TI  - On semilattices and lattices for families of theories
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 980
EP  - 985
VL  - 14
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a27/
LA  - en
ID  - SEMR_2017_14_a27
ER  - 
%0 Journal Article
%A S. V. Sudoplatov
%T On semilattices and lattices for families of theories
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 980-985
%V 14
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a27/
%G en
%F SEMR_2017_14_a27

[1] S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York, 2011 | MR

[2] G. W. Day, “Superatomic Boolean algebras”, Pacific J. Math., 23 (1967), 479–489 | DOI | MR | Zbl

[3] S. V. Sudoplatov, Combinations of structures, 2016, 19 pp., arXiv: 1601.00041v1 [math.LO]

[4] S. V. Sudoplatov, “Closures and generating sets related to combinations of structures”, Reports of Irkutsk State University. Series “Mathematics”, 16 (2016), 131–144 | Zbl

[5] S. V. Sudoplatov, “Families of language uniform theories and their generating sets”, Reports of Irkutsk State University. Series “Mathematics”, 17 (2016), 62–76 | Zbl

[6] S. V. Sudoplatov, “Relative $e$-spectra and relative closures for families of theories”, Siberian Electronic Mathematical Reports, 14 (2017), 296–307 | MR | Zbl