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Generalized r-cohesiveness and the arithmetical hierarchy: a correction to “Generalized cohesiveness”

Published online by Cambridge University Press:  12 March 2014

Carl G. Jockusch Jr.  and
Tamara J. Lakins
Carl G. Jockusch Jr.
Affiliation:
Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, IL 61801, USA, E-mail: [email protected]
Tamara J. Lakins
Affiliation:
Department of Mathematics, Allegheny College, 520 N. Main St., Meadville, PA 16335, USA, E-mail: [email protected]
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Abstract

For 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 1078 - 1082
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

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