Generalized r-cohesiveness and the arithmetical hierarchy: a correction to “Generalized cohesiveness”
AbstractFor X ⊆ ω, let [X]n denote the class of all n-element subsets of X. An infinite set A ⊆ ω is called n-r-cohesive if for each computable function f: [ω]n → {0, 1} there is a finite set F such that f is constant on [A − F]n. We show that for each n > 2 there is no Πn0 set A ⊆ ω which is n-r-cohesive. For n = 2 this refutes a result previously claimed by the authors, and for n ≥ 3 it answers a question raised by the authors.
1961 ◽
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1980 ◽
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1985 ◽
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2015 ◽
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