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From Eventually Different Functions to Pandemic Numberings

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Sailing Routes in the World of Computation (CiE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10936))

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Abstract

A function is strongly non-recursive (SNR) if it is eventually different from each recursive function. We obtain hierarchy results for the mass problems associated with computing such functions with varying growth bounds. In particular, there is no least and no greatest Muchnik degree among those of the form \({{\mathrm{SNR}}}_f\) consisting of SNR functions bounded by varying recursive bounds f.

We show that the connection between SNR functions and canonically immune sets is, in a sense, as strong as that between DNR (diagonally non-recursive) functions and effectively immune sets. Finally, we introduce pandemic numberings, a set-theoretic dual to immunity.

This work was partially supported by a grant from the Simons Foundation (#315188 to Bjørn Kjos-Hanssen).

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Authors and Affiliations

  1. University of Hawai‘i at Mānoa, Honolulu, HI, 96822, USA

    Achilles A. Beros, Mushfeq Khan & Bjørn Kjos-Hanssen

  2. University of Auckland, Auckland, New Zealand

    André Nies

Authors
  1. Achilles A. Beros
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  2. Mushfeq Khan
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  3. Bjørn Kjos-Hanssen
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  4. André Nies
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Corresponding author

Correspondence to Bjørn Kjos-Hanssen .

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Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Queens College, CUNY, Queens, New York, USA

    Russell G. Miller

  3. Kiel University, Kiel, Germany

    Dirk Nowotka

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Beros, A.A., Khan, M., Kjos-Hanssen, B., Nies, A. (2018). From Eventually Different Functions to Pandemic Numberings. In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_10

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  • DOI: https://doi.org/10.1007/978-3-319-94418-0_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94417-3

  • Online ISBN: 978-3-319-94418-0

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