IN MEMORIAM: GERALD E. SACKS, 1933–2019

Sacks’ work in that monograph covered many aspects of degree theory, and his innovative techniques produced several theorems that bear his name. [...]the importance of the results was equalled by the importance of the techniques he introduced. The degrees of unsolvability form an algebraic structure...

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Bibliographic Details
Published in:The bulletin of symbolic logic 2022-03, Vol.28 (1), p.150-155
Main Authors: Lerman, Manuel, Slaman, Theodore A.
Format: Article
Language:English
Subjects:
Computers
Hulls
In Memoriam
Innovations
Mathematics
Recursion theory
Sacks
Students
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Summary:Sacks’ work in that monograph covered many aspects of degree theory, and his innovative techniques produced several theorems that bear his name. [...]the importance of the results was equalled by the importance of the techniques he introduced. The degrees of unsolvability form an algebraic structure that provides a measure of the complexity of information inherent in an oracle attached to a computer. In his monograph, Sacks extended this method to $\Delta _{2}^{0}$ through his Sacks-preservation strategy; he showed that a noncomputable, computably enumerable set can be split into two sets of lesser information content, which together can compute the original set. [...]Sacks, together with his student Stephen Simpson [9], was able to obtain a solution combining the priority method with a method derived from model theory, Skolem hulls.
ISSN:1079-8986
1943-5894
DOI:10.1017/bsl.2022.8