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Workshop Thales Algebraic Modeling of Topological and Computational Structures and Applications

AlModTopCom 2015: Algebraic Modeling of Topological and Computational Structures and Applications pp 375–398Cite as

Generic Constructions and Generic Limits

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 219))

Abstract

We collect results related to generic constructions and generic limits for semantic and syntactic cases. It is considered both by pure model theory approach and by the institutional approach.

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Notes

  1. 1.

    Note that \(\mathbf{D}_0\) is closed under bijective substitutions since \(\preceq \) is preserved by bijective substitutions and \(\preceq \) is reflexive.

  2. 2.

    Note that \(\varPhi (A) \preceq \Psi (B)\) implies \(A \subseteq B\), since if \(a\in A\) then \((a\approx a)\in \varPhi (A)\), so \(\varPhi (A) \preceq \Psi (B)\) implies \(\varPhi (A) \subseteq \Psi (B)\) and we have \((a\approx a)\in \Psi (B)\), whence \(a\in B\).

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Acknowledgements

The first author was partially supported by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-6848.2016.1) and by Committee of Science in Education and Science Ministry of the Republic of Kazakhstan (Grant No. 0830/GF4). The second author was partially supported by Special Account for Research Grants of National Technical University of Athens.

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4, Acad. Koptyug Avenue, Novosibirsk, 630090, Russia

    Sergey V. Sudoplatov

  2. Novosibirsk State Technical University, 20, K.Marx Avenue, Novosibirsk, 630073, Russia

    Sergey V. Sudoplatov

  3. Novosibirsk State University, 2, Pirogova Street, Novosibirsk, 630090, Russia

    Sergey V. Sudoplatov

  4. Institute of Mathematics and Mathematical Modeling, 125, Pushkina Street, Almaty, 050010, Kazakhstan

    Sergey V. Sudoplatov

  5. Department of Applied Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Yiannis Kiouvrekis & Petros Stefaneas

Authors
  1. Sergey V. Sudoplatov
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  2. Yiannis Kiouvrekis
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  3. Petros Stefaneas
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Corresponding author

Correspondence to Sergey V. Sudoplatov .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, National Technical University of Athens, Athens, Greece

    Sofia Lambropoulou

  2. School of Chemical Engineering, National Technical University of Athens, Athens, Greece

    Doros Theodorou

  3. Department of Applied Mathematics, National Technical University of Athens, Athens, Greece

    Petros Stefaneas

  4. Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois, USA

    Louis H. Kauffman

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Sudoplatov, S.V., Kiouvrekis, Y., Stefaneas, P. (2017). Generic Constructions and Generic Limits. In: Lambropoulou, S., Theodorou, D., Stefaneas, P., Kauffman, L. (eds) Algebraic Modeling of Topological and Computational Structures and Applications. AlModTopCom 2015. Springer Proceedings in Mathematics & Statistics, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-68103-0_18

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