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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1752–1761
DOI: https://doi.org/10.33048/semi.2019.16.123 (Mi semr1164) 		 
Mathematical logic, algebra and number theory

Lattices in generative classes

Y. Kiouvrekisab, P. Stefaneasb, S. V. Sudoplatovcde

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
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DOI: https://doi.org/10.33048/semi.2019.16.123
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: lattice, generative class, generic structure, linear order, Boolean algebra.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP05132546
Siberian Branch of Russian Academy of Sciences I.1.1, project No. 0314-2019-0002
Russian Foundation for Basic Research 17-01-00531_a
European Science Foundation
This research is funded in the context of the project “MIS5005844” under the call for proposals “Supporting researchers with emphasis on new researchers” (EDULL 34). The project is co-financed by Greece and the European Union (European Social Fund- ESF) by the Operational Programme Human Resources Development, Education and Lifelong Learning 2014–2020. The third author was partially supported by Committee of Science in Education and Science Ministry of the Republic of Kazakhstan (Grant No. AP05132546), the program of fundamental scientific researches of the SB RAS No. I.1.1, project No. 0314-2019-0002, and Russian Foundation for Basic Researches (Project No. 17-01-00531-a).
Received February 11, 2019, published November 29, 2019
Bibliographic databases:
Document Type: Article
UDC: 510.67
MSC: 03C30, 03C45, 03C15, 03C52, 06B05
Language: English
Citation: Y. Kiouvrekis, P. Stefaneas, S. V. Sudoplatov, “Lattices in generative classes”, Sib. Èlektron. Mat. Izv., 16 (2019), 1752–1761
Citation in format AMSBIB
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\by Y.~Kiouvrekis, P.~Stefaneas, S.~V.~Sudoplatov
\paper Lattices in generative classes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1752--1761
\mathnet{http://mi.mathnet.ru/semr1164}
\crossref{https://doi.org/10.33048/semi.2019.16.123}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000501163400003}
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