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Kleene index sets and functional m-degrees

Published online by Cambridge University Press:  12 March 2014

Jeanleah Mohrherr
Jeanleah Mohrherr*
Affiliation:
University of Illinoisat Chicago, Circle Chicago, Illinois 60680
*
Cleveland State University, Cleveland, Ohio 44115
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Abstract

A many-one degree is functional if it contains the index set of some class of partial recursive functions but does not contain an index set of a class of r.e. sets. We give a natural embedding of the r.e. m-degrees into the functional degrees of 0′. There are many functional degrees in 0′ in the sense that every partial-order can be embedded. By generalizing, we show there are many functional degrees in every complete Turing degree.

There is a natural tie between the studies of index sets and partial-many-one reducibility. Every partial-many-one degree contains one or two index sets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 3 , September 1983 , pp. 829 - 840
Copyright
Copyright © Association for Symbolic Logic 1983

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