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Degrees with Almost Universal Cupping Property

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Book cover Programs, Proofs, Processes (CiE 2010)

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

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Abstract

The notion of cupping/noncupping has played an essential role in the study of various degree structures in the Ershov hierarchy. As an approach to refute Shoenfield conjecture, Yates (see [2]) proved the existence of a nonzero noncuppable r.e. degree, a degree cupping no incomplete r.e. degree to 0’. In contrast to this, Arslanov proved in [1] that nonzero noncuppable degrees do not exist in the structure of d.r.e. degrees, which shows that the structures of r.e. degrees and d.r.e. degrees are not elementary equivalent.

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References

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Authors and Affiliations

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

    Jiang Liu & Guohua Wu

Authors
  1. Jiang Liu
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  2. Guohua Wu
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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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Liu, J., Wu, G. (2010). Degrees with Almost Universal Cupping Property. 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_30

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

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