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Rice’s Theorem in Effectively Enumerable Topological Spaces

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Evolving Computability (CiE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9136))

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Abstract

In the framework of effectively enumerable topological spaces, we investigate the following question: given an effectively enumerable topological space whether there exists a computable numbering of all its computable elements. We present a natural sufficient condition on the family of basic neighborhoods of computable elements that guarantees the existence of a principal computable numbering. We show that weakly-effective \(\omega \)–continuous domains and the natural numbers with the discrete topology satisfy this condition. We prove weak and strong analogues of Rice’s theorem for computable elements.

This research was partially supported by Marie Curie Int. Research Staff Scheme Fellowship project PIRSES-GA-2011-294962, DFG/RFBR grant CAVER BE 1267/14-1 and 14-01-91334, RFBR grants 13-01-00015, 14-01-00376.

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Authors and Affiliations

  1. A.P. Ershov Institute of Informatics Systems, SbRAS, Novosibirsk, Russia

    Margarita Korovina

  2. Sobolev Institute of Mathematics, SbRAS, Novosibirsk, Russia

    Oleg Kudinov

Authors
  1. Margarita Korovina
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  2. Oleg Kudinov
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Correspondence to Margarita Korovina .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. University of Bucharest, Bucharest, Romania

    Victor Mitrana

  3. Sofia University, Sofia, Bulgaria

    Mariya Soskova

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Korovina, M., Kudinov, O. (2015). Rice’s Theorem in Effectively Enumerable Topological Spaces. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_23

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  • DOI: https://doi.org/10.1007/978-3-319-20028-6_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20027-9

  • Online ISBN: 978-3-319-20028-6

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