Wadge degrees of ω-languages of deterministic Turing machines
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 37 (2003) no. 1, p. 67-83

We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξ ω where ξ=ω 1 CK is the first non-recursive ordinal known as the Church-Kleene ordinal. This answers a question raised in [2].

DOI : https://doi.org/10.1051/ita:2003008
Classification:  03D55,  04A15,  68Q05
Keywords: hierarchy, Wadge degree, ω-language, ordinal, Turing machine, set-theoretic operation
@article{ITA_2003__37_1_67_0,
     author = {Selivanov, Victor},
     title = {Wadge degrees of $\sf \omega $-languages of deterministic Turing machines},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {1},
     year = {2003},
     pages = {67-83},
     doi = {10.1051/ita:2003008},
     zbl = {1048.03031},
     mrnumber = {1991752},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2003__37_1_67_0}
}
Selivanov, Victor. Wadge degrees of $\sf \omega $-languages of deterministic Turing machines. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 37 (2003) no. 1, pp. 67-83. doi : 10.1051/ita:2003008. http://www.numdam.org/item/ITA_2003__37_1_67_0/

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