This article is cited in 6 papers

Lattice of definability (of reducts) for integers with successor

A. L. Semenov^abc, S. F. Soprunov<sup>d

a</sup> 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.

UDC: 510.635

Received: 27.09.2020
Revised: 12.01.2021

DOI: 10.4213/im9107

 English version: Izvestiya: Mathematics, 2021, 85:6, 1257–1269

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