Abstract:
In this paper the lattice of definability for integers with a successor (the relation y=x+1) is described. The lattice, whose elements are also knows as reducts, consists of three
(naturally described) infinite series of relations.
The proof uses a version of the Svenonius theorem
for structures of special form.
This work was supported by the Russian Science Foundation (A. L. Semenov,
grant no. 17-11-01377, Sections 1, 3, and 5) and the Russian Foundation
for Basic Research (S. F. Soprunov, grant no. 19-29-14199, Sections 2 and 4).
Received: 27.09.2020 Revised: 12.01.2021
Bibliographic databases:
Document Type:
Article
UDC:510.635
Language: English
Original paper language: Russian
Citation:
A. L. Semenov, S. F. Soprunov, “Lattice of definability (of reducts) for integers with successor”, Izv. Math., 85:6 (2021), 1257–1269
\Bibitem{SemSop21}
\by A.~L.~Semenov, S.~F.~Soprunov
\paper Lattice of definability (of reducts) for integers with successor
\jour Izv. Math.
\yr 2021
\vol 85
\issue 6
\pages 1257--1269
\mathnet{http://mi.mathnet.ru/eng/im9107}
\crossref{https://doi.org/10.1070/IM9107}
\zmath{https://zbmath.org/?q=an:07480692}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021IzMat..85.1257S}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000745285900001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124241199}
Linking options:
https://www.mathnet.ru/eng/im9107
https://doi.org/10.1070/IM9107
https://www.mathnet.ru/eng/im/v85/i6/p245
This publication is cited in the following 5 articles:
A. L. Semenov, S. F. Soprunov, I. A. Ivanov-Pogodaev, “Creating new mathematics by schoolchildren”, Dokl. Math., 107:Suppl 1 (2023), S132–S136
V. V. Verbovskiy, A. D. Yershigeshova, “On o-stable Expansions of (Z,<,+)”, Lobachevskii J. Math., 44:12 (2023), 5485–5492
G. P. Amirdjanov, I. B. Gurevich, F. V. Kostyuk, N. S. Kulberg, T. A. Rudchenko, A. L. Semenov, A. N. Sotnikov, Yu. O. Trusova, A. Yu. Uvarov, V. A. Vardanyan, T. V. Yakovleva, V. V. Yashina, A. S. Zakharova, “The role of the Scientific Council “Cybernetics” of the USSR academy of sciences/the Russian academy of sciences in the development of national cybernetics and computer technology”, Pattern Recognit. Image Anal., 33:4 (2023), 988–1049
A. Semenov, S. Soprunov, “Automorphisms and definability (of reducts) for upward complete structures”, Mathematics, 10:20 (2022), 3748
A. L. Semenov, “Teoriya opredelimosti v kontekste informatsionno-kommunikatsionnykh sistem”, Matematicheskie osnovy informatiki i informatsionno-kommunikatsionnykh sistem, Tverskoi gosudarstvennyi universitet, Tver, 2021, 61–68
Citation in format AMSBIB
Contact us: