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Izvestiya: Mathematics, 2021, Volume 85, Issue 6, Pages 1257–1269
DOI: https://doi.org/10.1070/IM9107 (Mi im9107) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Lattice of definability (of reducts) for integers with successor

A. L. Semenovabc, S. F. Soprunovd

a Lomonosov Moscow State University
b Federal Research Center ‘Informatics and Control’ of Russian Academy of Science
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
d Centre of pedagogical workmanship
English version PDF (452 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM9107
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.
Keywords: definability, reducts, Svenonius theorem.
Funding agency Grant number
Russian Science Foundation 17-11-01377
Russian Foundation for Basic Research 19-29-14199
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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2021, Volume 85, Issue 6, Pages 245–258
DOI: https://doi.org/10.4213/im9107
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. RAN. Ser. Mat., 85:6 (2021), 245–258; Izv. Math., 85:6 (2021), 1257–1269
Citation in format AMSBIB
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\pages 245--258
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:27
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