Generalized R-Cohesiveness and the Arithmetical Hierarchy: A Correction to "Generalized Cohesiveness"

Journal of Symbolic Logic 67 (3):1078 - 1082 (2002)
For $X \subseteq \omega$ , let $\lbrack X \rbrack^n$ denote the class of all n-element subsets of X. An infinite set $A \subseteq \omega$ is called n-r-cohesive if for each computable function $f: \lbrack \omega \rbrack^n \rightarrow \lbrace 0, 1 \rbrace$ there is a finite set F such that f is constant on $\lbrack A - F \rbrack^n$ . We show that for each n ≥ 2 there is no $\prod_n^0$ set $A \subseteq \omega$ 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
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DOI 10.2178/jsl/1190150150
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