no. 1
On the hierarchies of Δ 2 0 -real numbers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 1, pp. 3-25.

A real number x is called Δ 2 0 if its binary expansion corresponds to a Δ 2 0 -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, Δ 2 0 -reals have different levels of effectiveness. This leads to various hierarchies of Δ 2 0 reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators.

DOI : 10.1051/ita:2007008
Classification : 03D55, 26E40, 68Q15
Mots clés : computably approximable reals, $\Delta ^0_2$-reals, hierarchy 
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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://www.numdam.org/articles/10.1051/ita:2007008/

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