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Computability and Complexity pp 127–133Cite as

Herrmann’s Beautiful Theorem on Computable Partial Orderings

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10010))

Abstract

We give an exposition of Herrmann’s proof that there is an infinite computable partial ordering with no infinite \(\Sigma ^0_2\) chains or antichains.

I am grateful to Eberhard Herrmann for finding the lovely proof on which this paper is based. I thank Rod Downey for his hospitality, collaboration, and support on my numerous trips to Wellington to work with him over the years. I also appreciate the opportunity to collaborate with him in many other places, including Urbana and Berkeley. Finally, I thank the Simons Foundation for supporting my travel to the meeting in New Zealand in 2017 in honor of his 60th birthday.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

    Carl G. Jockusch Jr.

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  1. Carl G. Jockusch Jr.
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Correspondence to Carl G. Jockusch Jr. .

Editor information

Editors and Affiliations

  1. Victoria University of Wellington, Wellington, New Zealand

    Adam Day

  2. University of Bergen, Bergen, Norway

    Michael Fellows

  3. Victoria University of Wellington, Wellington, New Zealand

    Noam Greenberg

  4. University of Auckland, Auckland, New Zealand

    Bakhadyr Khoussainov

  5. Massey University, Auckland, New Zealand

    Alexander Melnikov

  6. University of Bergen, Bergen, Norway

    Frances Rosamond

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Jockusch, C.G. (2017). Herrmann’s Beautiful Theorem on Computable Partial Orderings. In: Day, A., Fellows, M., Greenberg, N., Khoussainov, B., Melnikov, A., Rosamond, F. (eds) Computability and Complexity. Lecture Notes in Computer Science(), vol 10010. Springer, Cham. https://doi.org/10.1007/978-3-319-50062-1_10

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  • DOI: https://doi.org/10.1007/978-3-319-50062-1_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-50061-4

  • Online ISBN: 978-3-319-50062-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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