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Conference on Computability in Europe

CiE 2019: Computing with Foresight and Industry pp 84–95Cite as

Effective Embeddings for Pairs of Structures

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11558))

Abstract

We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. We show that computable embeddings induce a non-trivial degree structure for two-element classes consisting of computable structures, in particular the pair of linear orders \(\{\omega , \omega ^\star \}\), which are the order types of the positive integers and the negative integers, respectively.

The first author was partially supported by NSF Grant DMS #1600625, which allowed him to visit Sofia. The second and third authors were partially supported by BNSF Bilateral Grant DNTS/Russia 01/8 from 23.06.2017.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Nikolay Bazhenov

  2. Novosibirsk State University, Novosibirsk, Russia

    Nikolay Bazhenov

  3. Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier blvd., 1164, Sofia, Bulgaria

    Hristo Ganchev & Stefan Vatev

Authors
  1. Nikolay Bazhenov
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  2. Hristo Ganchev
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  3. Stefan Vatev
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Corresponding author

Correspondence to Stefan Vatev .

Editor information

Editors and Affiliations

  1. Christian Albrechts University of Kiel, Kiel, Germany

    Florin Manea

  2. Durham University, Durham, UK

    Barnaby Martin

  3. Durham University, Durham, UK

    Daniël Paulusma

  4. Università degli Studi di Milano, Milan, Italy

    Giuseppe Primiero

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Bazhenov, N., Ganchev, H., Vatev, S. (2019). Effective Embeddings for Pairs of Structures. In: Manea, F., Martin, B., Paulusma, D., Primiero, G. (eds) Computing with Foresight and Industry. CiE 2019. Lecture Notes in Computer Science(), vol 11558. Springer, Cham. https://doi.org/10.1007/978-3-030-22996-2_8

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  • DOI: https://doi.org/10.1007/978-3-030-22996-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22995-5

  • Online ISBN: 978-3-030-22996-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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