On the hierarchies of Δ20-real numbers

Xizhong Zheng

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 41, Issue: 1, page 3-25
  • ISSN: 0988-3754

Abstract

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A real number x is called Δ20 if its binary expansion corresponds to a Δ20-set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, Δ20-reals have different levels of effectiveness. This leads to various hierarchies of Δ20 reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators.

How to cite

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Zheng, Xizhong. "On the hierarchies of Δ20-real numbers." RAIRO - Theoretical Informatics and Applications 41.1 (2007): 3-25. <http://eudml.org/doc/250050>.

@article{Zheng2007,
abstract = { A real number x is called Δ20 if its binary expansion corresponds to a Δ20-set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, Δ20-reals have different levels of effectiveness. This leads to various hierarchies of Δ20 reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators. },
author = {Zheng, Xizhong},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Computably approximable reals; Δ20-reals; hierarchy.; computably approximable reals; -reals; hierarchy},
language = {eng},
month = {4},
number = {1},
pages = {3-25},
publisher = {EDP Sciences},
title = {On the hierarchies of Δ20-real numbers},
url = {http://eudml.org/doc/250050},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Zheng, Xizhong
TI - On the hierarchies of Δ20-real numbers
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/4//
PB - EDP Sciences
VL - 41
IS - 1
SP - 3
EP - 25
AB - A real number x is called Δ20 if its binary expansion corresponds to a Δ20-set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, Δ20-reals have different levels of effectiveness. This leads to various hierarchies of Δ20 reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators.
LA - eng
KW - Computably approximable reals; Δ20-reals; hierarchy.; computably approximable reals; -reals; hierarchy
UR - http://eudml.org/doc/250050
ER -

References

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