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

Section of Algebra and Mathematical Logic

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1752-1761
Number of pages	10
Journal	Сибирские электронные математические известия
Volume	16
DOIs	https://doi.org/10.33048/semi.2019.16.123
Publication status	Published - 1 Jan 2019

Keywords

Boolean algebra
Generative class
Generic structure
Lattice
Linear order

OECD FOS+WOS

1.01 MATHEMATICS

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10.33048/semi.2019.16.123

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