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Matematicheskie Zametki, 2020, Volume 108, Issue 1, Pages 102–118
DOI: https://doi.org/10.4213/mzm12651 (Mi mzm12651) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Lattice of Definability in the Order of Rational Numbers

An. A. Muchnika, A. L. Semenovbac

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
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DOI: https://doi.org/10.4213/mzm12651
Abstract: A lattice of definability subspaces in the order of rational numbers is described. It is proved that this lattice consists of five subspaces defined in the paper that are generated by the following relations: “equality,” “less,” “between,” “cycle,” and “linkage.” For each of the subspaces, its width (the minimum number of arguments of a generating relation) is found and a convenient description of the automorphism group is given. Although the structure of this lattice was known previously, the proof in the paper is of syntactic nature and avoids the use of a group-theoretical method.
Keywords: finitely generated space, lattice of definability subspaces, syntactic nature.
Funding agency Grant number
Russian Science Foundation 17-11-01377
This work was supported in part by the Russian Science Foundation under grant 17-11-01377.
Received: 20.02.2019
Revised: 22.07.2019
English version:
Mathematical Notes, 2020, Volume 108, Issue 1, Pages 94–107
DOI: https://doi.org/10.1134/S0001434620070093
Bibliographic databases:
Document Type: Article
UDC: 510.635
Language: Russian
Citation: An. A. Muchnik, A. L. Semenov, “Lattice of Definability in the Order of Rational Numbers”, Mat. Zametki, 108:1 (2020), 102–118; Math. Notes, 108:1 (2020), 94–107
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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