On the hierarchies of $\Delta ^0_2$-real numbers

Zheng, Xizhong

doi:10.1051/ita:2007008

On the hierarchies of

Δ_{2}^{0}

-real numbers

Zheng, Xizhong

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 1, pp. 3-25.

Résumé

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,

Δ_{2}^{0}

-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. https://www.numdam.org/articles/10.1051/ita:2007008/

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