A real number is called if its binary expansion corresponds to a -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, -reals have different levels of effectiveness. This leads to various hierarchies of reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators.
Mots-clés : computably approximable reals, $\Delta ^0_2$-reals, hierarchy
@article{ITA_2007__41_1_3_0, author = {Zheng, Xizhong}, title = {On the hierarchies of $\Delta ^0_2$-real numbers}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {3--25}, publisher = {EDP-Sciences}, volume = {41}, number = {1}, year = {2007}, doi = {10.1051/ita:2007008}, mrnumber = {2330040}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2007008/} }
TY - JOUR AU - Zheng, Xizhong TI - On the hierarchies of $\Delta ^0_2$-real numbers JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2007 SP - 3 EP - 25 VL - 41 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2007008/ DO - 10.1051/ita:2007008 LA - en ID - ITA_2007__41_1_3_0 ER -
%0 Journal Article %A Zheng, Xizhong %T On the hierarchies of $\Delta ^0_2$-real numbers %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2007 %P 3-25 %V 41 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2007008/ %R 10.1051/ita:2007008 %G en %F ITA_2007__41_1_3_0
Zheng, Xizhong. On the hierarchies of $\Delta ^0_2$-real numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 1, pp. 3-25. doi : 10.1051/ita:2007008. http://archive.numdam.org/articles/10.1051/ita:2007008/
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