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A MINIMAL PAIR IN THE GENERIC DEGREES

Published online by Cambridge University Press:  12 November 2019

DENIS R. HIRSCHFELDT
DENIS R. HIRSCHFELDT*
Affiliation:
DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF CHICAGO CHICAGO, IL, USA E-mail: drh@math.uchicago.edu
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Abstract

We show that there is a minimal pair in the nonuniform generic degrees, and hence also in the uniform generic degrees. This fact contrasts with Igusa’s result that there are no minimal pairs for relative generic computability and answers a basic structural question mentioned in several papers in the area.

Keywords

03D30generic computabilitygeneric reducibilityminimal pairs
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 1 , March 2020 , pp. 531 - 537
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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