Degrees of Unsolvability: A Survey of Results

Publisher Summary The structure of the degrees is essentially a classification of all sets of integers according to complexity. The recursive sets of integers comprise the lowest level of complexity. A “degree” is just an equivalence class of sets of integers, under the following equivalence relation: S 1 is recursive relative to S 2 , and S 2 is recursive relative to S 1 . This chapter presents the theorems whose statements highlight the structure and uses of degrees. The chapter also discusses the structure of the degrees without jump, the jump operator, and degrees of complete theories.

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