## Journal of Symbolic Logic

### Kleene Index Sets and Functional $m$-Degrees

Jeanleah Mohrherr

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 48, Issue 3 (1983), 829-840.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741343

Mathematical Reviews number (MathSciNet)
MR716645

Zentralblatt MATH identifier
0538.03038

JSTOR
Mohrherr, Jeanleah. Kleene Index Sets and Functional $m$-Degrees. J. Symbolic Logic 48 (1983), no. 3, 829--840. https://projecteuclid.org/euclid.jsl/1183741343