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Kleene Index Sets and Functional m-Degrees

Jeanleah Mohrherr
The Journal of Symbolic Logic
Vol. 48, No. 3 (Sep., 1983), pp. 829-840
DOI: 10.2307/2273476
Stable URL: http://www.jstor.org/stable/2273476
Page Count: 12
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Kleene Index Sets and Functional m-Degrees
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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 Turning 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.

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