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This article is cited in 11 scientific papers (total in 11 papers)
Some presentations of the real number field
A. S. Morozovab
a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract:
It is proved that every two $\Sigma$-presentations of an ordered field $\mathbb R$ of reals
over $\mathbb{HF(R)}$, whose universes are subsets of $\mathbb R$, are mutually $\Sigma$-isomorphic. As
a consequence, for a series of functions $f\colon\mathbb R\to\mathbb R$ (e.g., $\exp$, $\sin$, $\cos$, $\ln$), it is stated that the structure $\mathbb R=\langle R,+,\times,<,0,1,f\rangle$ lacks such $\Sigma$-presentations
over $\mathbb{HF(R)}$.
Keywords:
$\Sigma$-presentation, ordered field of reals.
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English version:
Algebra and Logic, 2012, 51:1, 66–88
Bibliographic databases:
   
UDC:
510.6+510.5
Received: 26.03.2011
Revised: 08.11.2011
Citation:
A. S. Morozov, “Some presentations of the real number field”, Algebra Logika, 51:1 (2012), 96–128; Algebra and Logic, 51:1 (2012), 66–88
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/al524 http://mi.mathnet.ru/eng/al/v51/i1/p96
Citing articles on Google Scholar:
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English citations
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Cycle of papers
This publication is cited in the following articles:
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A. S. Morozov, “Nonpresentability of the semigroup $\omega^\omega$ over $\mathbb{HF(R)}$”, Siberian Math. J., 55:1 (2014), 125–131
 -
S. A. Aleksandrova, “The uniformization problem for $\Sigma$-predicates in a hereditarily finite list superstructure over the real exponential field”, Algebra and Logic, 53:1 (2014), 1–8
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A. S. Morozov, “On $\Sigma$-rigid presentations of the real order”, Siberian Math. J., 55:3 (2014), 457–464
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A. S. Morozov, “$\Sigma$-presentations of the ordering on the reals”, Algebra and Logic, 53:3 (2014), 217–237
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A. S. Morozov, “A sufficient condition for nonpresentability of structures in hereditarily finite superstructures”, Algebra and Logic, 55:3 (2016), 242–251
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A. S. Morozov, “Computable model theory over the reals”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, ed. A. Day, M. Fellows, N. Greenberg, B. Khoussainov, A. Melnikov, F. Rosamond, Springler, 2017, 354–365
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A. S. Morozov, “Nonpresentability of some structures of analysis in hereditarily finite superstructures”, Algebra and Logic, 56:6 (2018), 458–472
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S. A. Aleksandrova, “O $\Sigma$-opredelimosti nasledstvenno konechnoi i spisochnoi nadstroek”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 3–10
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Greenberg N., Melnikov A.G., Knight J.F., Turetsky D., “Uniform Procedures in Uncountable Structures”, J. Symb. Log., 83:2 (2018), 529–550
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A. S. Morozov, “$\Sigma$-preorderings in ${\mathbb{HF}(\mathbb{R})}$”, Algebra and Logic, 58:5 (2019), 405–416
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R. M. Korotkova, O. V. Kudinov, A. S. Morozov, “On mutual definability of operations on fields”, Siberian Math. J., 60:6 (2019), 1032–1039
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