Journal of Symbolic Logic 59 (1):166-181 (1994)

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
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DOI 10.2307/2275258
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Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.

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