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Σ-Presentations of the Ordering on the Reals

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Algebra and Logic Aims and scope

We prove the nonexistence of universal Σ-presentable linear orderings as well as the effective infinity of the class of Σ-presentations of the natural order on ℝ over an admissible set ℍ\( \mathbb{F} \)(ℝ).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. S. Morozov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. S. Morozov

Authors
  1. A. S. Morozov
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Correspondence to A. S. Morozov.

Additional information

*Supported by RFBR (project No. 11-01-00236) and by the Federal Program “Scientific and Scientific-Pedagogical Cadres of Innovative Russia” for 2009-2013 (project No. 8227).

Translated from Algebra i Logika, Vol. 53, No. 3, pp. 340-371, May-June, 2014.

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Morozov, A.S. Σ-Presentations of the Ordering on the Reals. Algebra Logic 53, 217–237 (2014). https://doi.org/10.1007/s10469-014-9285-6

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  • DOI: https://doi.org/10.1007/s10469-014-9285-6

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