The members of thin and minimal [formula omitted] classes, their ranks and Turing degrees

Rodney G Downey,Guohua Wu,Yue Yang

doi:10.1016/j.apal.2015.03.004

The members of thin and minimal [formula omitted] classes, their ranks and Turing degrees

Rodney G Downey, Guohua Wu + Show 1 more

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https://doi.org/10.1016/j.apal.2015.03.004

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Journal: Annals of Pure and Applied Logic	Publication Date: Apr 1, 2015
Citations: 2	License type: elsevier-specific: oa user license

Affiliation: Victoria University of Wellington, Nanyang Technological University, National University of Singapore

#Turing Degrees #Cantor Bendixson Ranks + Show 4 more

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Abstract

We study the relationship among members of Π10 classes, thin Π10 classes, their Cantor–Bendixson ranks and their Turing degrees; in particular, we show that any nonzero Δ20 degree contains a member of rank α for any computable ordinal α. Furthermore we observe that the degrees containing members of thin Π10 classes are not closed under join.

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