Low sets without subsets of higher many-one degree

Mathematical Logic Quarterly 57 (5):517-523 (2011)
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Abstract

Given a reducibility ⩽r, we say that an infinite set A is r-introimmune if A is not r-reducible to any of its subsets B with |A\B| = ∞. We consider the many-one reducibility ⩽m and we prove the existence of a low1 m-introimmune set in Π01 and the existence of a low1 bi-m-introimmune set

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10.1002/malq.200920043

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Patrizio Cintioli
Università degli Studi di Camerino

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References found in this work

A cohesive set which is not high.Carl Jockusch & Frank Stephan - 1993 - Mathematical Logic Quarterly 39 (1):515-530.
Sets with no subset of higher degrees.Robert I. Soare - 1969 - Journal of Symbolic Logic 34 (1):53-56.
Sets which do not have subsets of every higher degree.Stephen G. Simpson - 1978 - Journal of Symbolic Logic 43 (1):135-138.
A note on degrees of subsets.Robert I. Soare - 1969 - Journal of Symbolic Logic 34 (2):256.

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