Geodesic
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. 
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     title = {On semilattices and lattices for families of theories},
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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/

[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