---
_id: '18280'
abstract:
- lang: eng
  text: The sometimes so-called Main Theorem of Recursive Analysis implies that any
    computable real function is necessarily continuous. We consider three relaxations
    of this common notion of real computability for the purpose of treating also discontinuous
    functions f:R->R:<br>*) non-deterministic computation;<br>*) relativized computation,
    specifically given access to oracles like 0' or 0'';<br>*) encoding input x and/or
    output y=f(x) in weaker ways according to the Real Arithmetic Hierarchy.<br>It
    turns out that, among these approaches, only the first one provides the required
    power.
author:
- first_name: Martin
  full_name: Ziegler, Martin
  last_name: Ziegler
citation:
  ama: 'Ziegler M. Computability and Continuity on the Real Arithmetic Hierarchy and
    the Power of Type-2 Nondeterminism. In: <i>Proc. CiE 2005: New Computational Paradigms</i>.
    Vol 3526. Springer; 2005:562-571. doi:<a href="https://doi.org/10.1007/11494645_68">10.1007/11494645_68</a>'
  apa: 'Ziegler, M. (2005). Computability and Continuity on the Real Arithmetic Hierarchy
    and the Power of Type-2 Nondeterminism. In <i>Proc. CiE 2005: New Computational
    Paradigms</i> (Vol. 3526, pp. 562–571). Springer. <a href="https://doi.org/10.1007/11494645_68">https://doi.org/10.1007/11494645_68</a>'
  bibtex: '@inproceedings{Ziegler_2005, title={Computability and Continuity on the
    Real Arithmetic Hierarchy and the Power of Type-2 Nondeterminism}, volume={3526},
    DOI={<a href="https://doi.org/10.1007/11494645_68">10.1007/11494645_68</a>}, booktitle={Proc.
    CiE 2005: New Computational Paradigms}, publisher={Springer}, author={Ziegler,
    Martin}, year={2005}, pages={562–571} }'
  chicago: 'Ziegler, Martin. “Computability and Continuity on the Real Arithmetic
    Hierarchy and the Power of Type-2 Nondeterminism.” In <i>Proc. CiE 2005: New Computational
    Paradigms</i>, 3526:562–71. Springer, 2005. <a href="https://doi.org/10.1007/11494645_68">https://doi.org/10.1007/11494645_68</a>.'
  ieee: 'M. Ziegler, “Computability and Continuity on the Real Arithmetic Hierarchy
    and the Power of Type-2 Nondeterminism,” in <i>Proc. CiE 2005: New Computational
    Paradigms</i>, 2005, vol. 3526, pp. 562–571.'
  mla: 'Ziegler, Martin. “Computability and Continuity on the Real Arithmetic Hierarchy
    and the Power of Type-2 Nondeterminism.” <i>Proc. CiE 2005: New Computational
    Paradigms</i>, vol. 3526, Springer, 2005, pp. 562–71, doi:<a href="https://doi.org/10.1007/11494645_68">10.1007/11494645_68</a>.'
  short: 'M. Ziegler, in: Proc. CiE 2005: New Computational Paradigms, Springer, 2005,
    pp. 562–571.'
date_created: 2020-08-25T12:38:49Z
date_updated: 2022-01-06T06:53:28Z
department:
- _id: '63'
doi: 10.1007/11494645_68
intvolume: '      3526'
language:
- iso: eng
page: 562-571
publication: 'Proc. CiE 2005: New Computational Paradigms'
publication_identifier:
  isbn:
  - '9783540261797'
  - '9783540322665'
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer
status: public
title: Computability and Continuity on the Real Arithmetic Hierarchy and the Power
  of Type-2 Nondeterminism
type: conference
user_id: '15415'
volume: 3526
year: '2005'
...