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Conference on Computability in Europe

CiE 2022: Revolutions and Revelations in Computability pp 234–245Cite as

On Trees Without Hyperimmune Branches

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13359))

Abstract

The current work includes a result announced in the year 2012 which was unproven until now. The result shows that there is a co-r.e. tree with uncountably many infinite branches such that the nonisolated infinite branches of the constructed tree are all nonrecursive, generalised low, hyperimmune-free and form a perfect tree.

Frank Stephan and Yang Yue have been supported in part by the Singapore Ministry of Education Tier 2 grant AcRF MOE2019-T2-2-121/R146-000-304-112 as well as by the NUS Tier 1 grants AcRF R146-000-337-114 and R252-000-C17-114. Keng Meng Ng is supported by the Singapore Ministry of Education grant RG23/19 at NTU. Liang Yu was supported by NSFC grant No. 12025103.

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Republic of Singapore

    Keng Meng Ng

  2. School of Computing, National University of Singapore, 13 Computing Drive, Block COM1, Singapore, 117417, Republic of Singapore

    Frank Stephan

  3. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Block S17, Singapore, 119076, Republic of Singapore

    Frank Stephan & Yue Yang

  4. Mathematical Department, Nanjing University, Nanjing, 210093, Jiangsu, People’s Republic of China

    Liang Yu

Authors
  1. Keng Meng Ng
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  2. Frank Stephan
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  3. Yue Yang
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  4. Liang Yu
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Corresponding author

Correspondence to Frank Stephan .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, UK

    Ulrich Berger

  2. Department of Mathematics, Hofstra University, Hempstead, NY, USA

    Johanna N. Y. Franklin

  3. Georg-August University Göttingen, Göttingen, Germany

    Florin Manea

  4. Department of Computer Science, Swansea University, Swansea, UK

    Arno Pauly

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Ng, K.M., Stephan, F., Yang, Y., Yu, L. (2022). On Trees Without Hyperimmune Branches. In: Berger, U., Franklin, J.N.Y., Manea, F., Pauly, A. (eds) Revolutions and Revelations in Computability. CiE 2022. Lecture Notes in Computer Science, vol 13359. Springer, Cham. https://doi.org/10.1007/978-3-031-08740-0_20

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  • DOI: https://doi.org/10.1007/978-3-031-08740-0_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08739-4

  • Online ISBN: 978-3-031-08740-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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