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On Elementary and Geometric Equivalence of Equational Co-Domains

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Abstract

We prove that the class of equational co-domains is not closed under elementary and geometric equivalence. We find corresponding counter-examples in predicate and functional languages.

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References

  1. E. Yu. Daniyarova, A. G. Myasnikov, and V. N. Remeslennikov, Algebraic Geometry over Algebraic Structures [in Russian], Novosibirsk, SO RAN (2016).

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  2. E. Yu. Daniyarova, A. G. Myasnikov, and V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VIII. Geometric equivalences and classes of algebraic structures,” Fundam. Prikl. Mat., 22, No. 4 (2019).

  3. A. N. Shevlyakov, Lectures Notes in Universal Algebraic Geometry, arXiv:1601.02743.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Pevtsova st. 13, Omsk, 644099, Russia

    A. N. Shevlyakov

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  1. A. N. Shevlyakov
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Correspondence to A. N. Shevlyakov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 4, pp. 229–238, 2019.

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Shevlyakov, A.N. On Elementary and Geometric Equivalence of Equational Co-Domains. J Math Sci 257, 902–908 (2021). https://doi.org/10.1007/s10958-021-05529-6

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  • DOI: https://doi.org/10.1007/s10958-021-05529-6

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