A rank one cohesive set

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Abstract

In this paper, we prove that there is a Π01 class in 2ω with a unique nonrecursive member, with that member a cohesive set. This solves an open question from Cenzer (1993). The proof uses the Δ03 method in the context of the construction of a Π01 class.

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Research supported by the Lee Foundation which partially supported a visit by Downey to the National University of Singapore during January 1993, while on his sabbatical leave from Victoria University.