Mathematical Logic Quarterly

The Index Set of Injectively Enumerable Classes of Recursively Enumerable Sets in ∑ 5 ‐Complete

Journal Article


I introduce an effective enumeration of all effective enumerations of classes of r. e. sets and define with this the index set IE of injectively enumerable classes. It is easy to see that this set is ∑5 in the Arithmetical Hierarchy and I describe a proof for the ∑5‐hardness of IE.

Mathematics Subject Classification: 03D25, 03D45.

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