Y. Kiouvrekis, P. Stefaneas, S. V. Sudoplatov, “Lattices in generative classes”, Сиб. электрон. матем. изв., 2019, том 16,страницы 1752

Математическая логика, алгебра и теория чисел

Lattices in generative classes

Y. Kiouvrekis^ab, P. Stefaneas^b, S. V. Sudoplatov^cde

^a University of Thessaly, Medical Department, Laboratory of Medical Physics and Informatics, Thessaly, Greece
^b National Technical University of Athens, Department of Mathematics, 9, Herron Polytechniou, Zografou, 15780, Greece
^c Sobolev Institute of Mathematics, 4, Academician Koptyug ave., Novosibirsk, 630090, Russia
^d Novosibirsk State Technical University, 20, K. Marx ave., Novosibirsk, 630073, Russia
^e Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Аннотация: 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.

Ключевые слова: lattice, generative class, generic structure, linear order, Boolean algebra.

УДК: 510.67

MSC: 03C30, 03C45, 03C15, 03C52, 06B05

Поступила 11 февраля 2019 г., опубликована 29 ноября 2019 г.

Язык публикации: английский

DOI: 10.33048/semi.2019.16.123