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Chebyshevskii Sbornik, 2021, Volume 22, Issue 1, Pages 304–327
DOI: https://doi.org/10.22405/2226-8383-2018-22-1-304-327 (Mi cheb1003) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The lattice of definability. Origins and directions of research

A. L. Semenovab, S. F. Soprunovcb

a Lomonosov Moscow State University (Moscow)
b Axel Berg Institute of Cybernetics and Educational Computing FRC SCS of the Russian Academy of Sciences (Moscow)
c Center for pedagogical excellence (Moscow)
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DOI: https://doi.org/10.22405/2226-8383-2018-22-1-304-327
Abstract: The article presents results and open problems related to definability spaces (reducts) and sources of this field since the XIX century. Finiteness conditions and constraints are investigated, including the depth of quantifier alternation and the number of arguments. Results related to the description of lattices of definability spaces for numerical and other natural structures are described. Research methods include the study of automorphism groups of elementary extensions of the structures under consideration, application of the Svenonius theorem.
Keywords: definability, definability space, reducts, Svenonius theorem, quantifier elimination, decidability, automorphisms.
Funding agency Grant number
Russian Science Foundation 17-11-01377
Russian Foundation for Basic Research 19-29-14199
Received: 20.12.2020
Accepted: 21.02.2021
English version:
Doklady Mathematics (Supplementary issues), 2022, Volume 106, Issue 2, Pages 288–298
DOI: https://doi.org/10.1134/S1064562423700370
Document Type: Article
UDC: 517
Language: Russian
Citation: A. L. Semenov, S. F. Soprunov, “The lattice of definability. Origins and directions of research”, Chebyshevskii Sb., 22:1 (2021), 304–327; Doklady Mathematics (Supplementary issues), 106:2 (2022), 288–298
Citation in format AMSBIB
\Bibitem{SemSop21}
\by A.~L.~Semenov, S.~F.~Soprunov
\paper The lattice of definability. Origins and directions of research
\jour Chebyshevskii Sb.
\yr 2021
\vol 22
\issue 1
\pages 304--327
\mathnet{http://mi.mathnet.ru/cheb1003}
\crossref{https://doi.org/10.22405/2226-8383-2018-22-1-304-327}
\transl
\jour Doklady Mathematics (Supplementary issues)
\yr 2022
\vol 106
\issue 2
\pages 288--298
\crossref{https://doi.org/10.1134/S1064562423700370}
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    • This publication is cited in the following 1 articles:
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