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Conference on Computability in Europe

CiE 2010: Programs, Proofs, Processes pp 219–228Cite as

On Index Sets of Some Properties of Computable Algebras

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6158))

Abstract

We study the index sets of the following properties of computable algebras: to have no nontrivial congruences, to have a finite number of congruences, to have infinite decreasing or increasing chains of congruence relations. We prove completeness of these index sets in arithmetic and hyperarithmetic hierarchies.

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Author information

Authors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Bakhadyr Khoussainov

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Andrey Morozov

Authors
  1. Bakhadyr Khoussainov
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  2. Andrey Morozov
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Fernando Ferreira

  2. Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, P.O. Box 94242, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  3. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna 1, 50018, Zaragoza, Spain

    Elvira Mayordomo

  4. Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal

    Luís Mendes Gomes

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Khoussainov, B., Morozov, A. (2010). On Index Sets of Some Properties of Computable Algebras. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_25

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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