Soare and Simpson considered sets without subsets of higher Turing degree. In this paper we consider sets which are not many-one reducible to any of their subsets, which are set without subsets without subsets of higher many-one degree, and examine how structurally easy can be such sets. In other words, we ask what is the smallest class of the Kleenes Hierarchy containing such sets. We prove that the smallets such class is the class of the co-r.e. sets.

Sets without subsets of higher many-one degree

CINTIOLI, Patrizio
2005

Abstract

Soare and Simpson considered sets without subsets of higher Turing degree. In this paper we consider sets which are not many-one reducible to any of their subsets, which are set without subsets without subsets of higher many-one degree, and examine how structurally easy can be such sets. In other words, we ask what is the smallest class of the Kleenes Hierarchy containing such sets. We prove that the smallets such class is the class of the co-r.e. sets.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11581/202733
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