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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
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.
Received: 27.09.2020 Revised: 12.01.2021
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
Linking options:
https://www.mathnet.ru/eng/im9107https://doi.org/10.1070/IM9107 https://www.mathnet.ru/eng/im/v85/i6/p245
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Abstract page: | 608 | Russian version PDF: | 100 | English version PDF: | 27 | Russian version HTML: | 188 | References: | 33 | First page: | 12 |
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