Geodesic
Lattices in generative classes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1752-1761

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We define and study lattices in generative classes associated with generic structures. It is shown that these lattices can be non-distributive and, moreover, arbitrary enough. Heights and wights of the lattices are described. A model-theoretic criterion for the linear ordering is proved and these linear orders are described. Boolean algebras generated by the considered lattices are also described.
Keywords: lattice, generative class, generic structure, linear order, Boolean algebra. 
@article{SEMR_2019_16_a27,
     author = {Y. Kiouvrekis and P. Stefaneas and S. V. Sudoplatov},
     title = {Lattices in generative classes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1752--1761},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a27/}
}
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Y. Kiouvrekis; P. Stefaneas; S. V. Sudoplatov. Lattices in generative classes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1752-1761. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a27/