Lattices in generative classes

Yiannis Kiouvrekis; Petros Stefaneas; Sergey Vladimirovich Sudoplatov

doi:10.33048/semi.2019.16.123

Lattices in generative classes

Yiannis Kiouvrekis, Petros Stefaneas, Sergey Vladimirovich Sudoplatov

Кафедра алгебры и математической логики ММФ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

1 Цитирования (Scopus)

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.

Язык оригинала	английский
Страницы (с-по)	1752-1761
Число страниц	10
Журнал	Сибирские электронные математические известия
Том	16
DOI	https://doi.org/10.33048/semi.2019.16.123
Состояние	Опубликовано - 1 янв. 2019

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10.33048/semi.2019.16.123

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title = "Lattices in generative classes",

abstract = "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 = "Boolean algebra, Generative class, Generic structure, Lattice, Linear order",

author = "Yiannis Kiouvrekis and Petros Stefaneas and Sudoplatov, {Sergey Vladimirovich}",

year = "2019",

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doi = "10.33048/semi.2019.16.123",

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Lattices in generative classes. / Kiouvrekis, Yiannis; Stefaneas, Petros; Sudoplatov, Sergey Vladimirovich.

В: Сибирские электронные математические известия, Том 16, 01.01.2019, стр. 1752-1761.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

TY - JOUR

T1 - Lattices in generative classes

AU - Kiouvrekis, Yiannis

AU - Stefaneas, Petros

AU - Sudoplatov, Sergey Vladimirovich

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Boolean algebra

KW - Generative class

KW - Generic structure

KW - Lattice

KW - Linear order

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U2 - 10.33048/semi.2019.16.123

DO - 10.33048/semi.2019.16.123

M3 - Article

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VL - 16

SP - 1752

EP - 1761

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

Lattices in generative classes

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