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Algebra Logika, 2012, Volume 51, Number 1, Pages 96–128 (Mi al524)  

This article is cited in 9 scientific papers (total in 9 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.

Full text: PDF file (302 kB)
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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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\paper Some presentations of the real number field
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\issue 1
\pages 96--128
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\yr 2012
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\pages 66--88
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. A. S. Morozov, “Nonpresentability of the semigroup $\omega^\omega$ over $\mathbb{HF(R)}$”, Siberian Math. J., 55:1 (2014), 125–131  mathnet  crossref  mathscinet  isi
    2. 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  mathnet  crossref  mathscinet  isi
    3. A. S. Morozov, “On $\Sigma$-rigid presentations of the real order”, Siberian Math. J., 55:3 (2014), 457–464  mathnet  crossref  mathscinet  isi  elib  elib
    4. A. S. Morozov, “$\Sigma$-presentations of the ordering on the reals”, Algebra and Logic, 53:3 (2014), 217–237  mathnet  crossref  mathscinet  isi
    5. A. S. Morozov, “A sufficient condition for nonpresentability of structures in hereditarily finite superstructures”, Algebra and Logic, 55:3 (2016), 242–251  mathnet  crossref  crossref  isi
    6. 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  crossref  mathscinet  zmath  isi  scopus
    7. A. S. Morozov, “Nonpresentability of some structures of analysis in hereditarily finite superstructures”, Algebra and Logic, 56:6 (2018), 458–472  mathnet  crossref  crossref  isi
    8. S. A. Aleksandrova, “O $\Sigma$-opredelimosti nasledstvenno konechnoi i spisochnoi nadstroek”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 3–10  mathnet  crossref
    9. Greenberg N., Melnikov A.G., Knight J.F., Turetsky D., “Uniform Procedures in Uncountable Structures”, J. Symb. Log., 83:2 (2018), 529–550  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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