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Algebra Logika, 2014, Volume 53, Number 3, Pages 340–371 (Mi al639)  

This article is cited in 3 scientific papers (total in 3 papers)

$\Sigma$-presentations of the ordering on the reals

A. S. Morozovab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: We prove the nonexistence of universal $\Sigma$-presentable linear orderings as well as the effective infinity of the class of $\Sigma$-presentations of the natural order on $\mathbb R$ over an admissible set $\mathbb{HF(R)}$.

Keywords: $\Sigma$-presentation, ordering on reals, admissible set.

Full text: PDF file (320 kB)
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English version:
Algebra and Logic, 2014, 53:3, 217–237

Bibliographic databases:

UDC: 510.65
Received: 10.10.2012
Revised: 13.03.2014

Citation: A. S. Morozov, “$\Sigma$-presentations of the ordering on the reals”, Algebra Logika, 53:3 (2014), 340–371; Algebra and Logic, 53:3 (2014), 217–237

Citation in format AMSBIB
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\by A.~S.~Morozov
\paper $\Sigma$-presentations of the ordering on the reals
\jour Algebra Logika
\yr 2014
\vol 53
\issue 3
\pages 340--371
\mathnet{http://mi.mathnet.ru/al639}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3288441}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 3
\pages 217--237
\crossref{https://doi.org/10.1007/s10469-014-9285-6}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84922005037}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    3. S. A. Aleksandrova, “O $\Sigma$-opredelimosti nasledstvenno konechnoi i spisochnoi nadstroek”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 3–10  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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