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Generalized Effective Reducibility

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2016

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Carl, Merlin

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https://doi.org/10.1007/978-3-319-40189-8_23
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BECKMANN, Arnold, ed. and others. Pursuit of the Universal : 12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016; Proceedings. Cham: Springer, 2016, pp. 225-233. Lecture Notes in Computer Science. 9709. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-40188-1. Available under: doi: 10.1007/978-3-319-40189-8_23

Zusammenfassung

We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch reducibility. We give sample applications by showing that certain (algebraic) constructions are not effective in the OTM-sense and considering the effective equivalence of various versions of the axiom of choice.

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510 Mathematik

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12th Conference on Computability in Europe, CiE 2016, 27. Juni 2016 - 1. Juli 2016, Paris
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ISO 690CARL, Merlin, 2016. Generalized Effective Reducibility. 12th Conference on Computability in Europe, CiE 2016. Paris, 27. Juni 2016 - 1. Juli 2016. In: BECKMANN, Arnold, ed. and others. Pursuit of the Universal : 12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016; Proceedings. Cham: Springer, 2016, pp. 225-233. Lecture Notes in Computer Science. 9709. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-40188-1. Available under: doi: 10.1007/978-3-319-40189-8_23
BibTex
@inproceedings{Carl2016-06-14Gener-39703,
  year={2016},
  doi={10.1007/978-3-319-40189-8_23},
  title={Generalized Effective Reducibility},
  number={9709},
  isbn={978-3-319-40188-1},
  issn={0302-9743},
  publisher={Springer},
  address={Cham},
  series={Lecture Notes in Computer Science},
  booktitle={Pursuit of the Universal : 12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016; Proceedings},
  pages={225--233},
  editor={Beckmann, Arnold},
  author={Carl, Merlin}
}
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