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The degrees of conditional problems

Published online by Cambridge University Press:  12 March 2014

Su Gao
Su Gao*
Affiliation:
Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90024, E-mail: sgao@math.ucla.edu
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Abstract

In this paper we define and study conditional problems and their degrees. The main result is that the class of conditional degrees is a lattice extending the ordinary Turing degrees and it is dense. These properties are not shared by ordinary Turing degrees. We show that the class of conditional many-one degrees is a distributive lattice. We also consider properties of semidecidable problems and their degrees, which are analogous to r.e. sets and degrees.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 166 - 181
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

[1]Soare, Robert I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, Heidelberg, New York, 1984.Google Scholar
[2]Lerman, Manuel, Degrees of unsolvability, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983.CrossRefGoogle Scholar
[3]Rogers, Hartley Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar