Geodesic
Initial Segments of Many-One Degrees
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 75-85

Voir la notice de l'article provenant de la source Cambridge University Press

Our aim in this paper is to give a characterization of the order types of the countable initial segments of many-one degrees (m-degrees). The basic definitions and background information can be found in [2] from where we draw most of our notation and terminology. We expand the usual notion of m-reducibility by adopting the convention that R ≦m ∅ and R ≦mN for every recursive set R. This has the effect of giving all recursive sets the same m-degree; that m-degree will be denoted by 0. We shall denote by ≦ the partial ordering of m-degrees induced by ≦m, and shall denote by a ∪ b the least upper bound of the m-degrees a, b. We call a ∪ b the union of a and b. 
Lachlan, A. H. Initial Segments of Many-One Degrees. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 75-85. doi: 10.4153/CJM-1970-010-6
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[1] 1. Lachlan, A. H., Distributive initial segments of the degrees of unsolvability, Z. Math. Logik Grundlagen Math. 14 (1968), 457–472. Google Scholar

[2] 2. Rogers, H. Jr., Theory of recursive functions and effective computability (McGraw-Hill, New York, 1967). Google Scholar

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