The Degrees of Hyperimmune Sets

Miller, W. A.; Martin, Donald A.

doi:10.1002/malq.19680140704

Cited by 77 publications

(53 citation statements)

References 6 publications

(4 reference statements)

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“…On the other hand, Bedregal and Nies [3] have shown that if A is Low(CR) then A has hyperimmune-free degree (also see [13]). The only 0 2 sets of hyperimmune-free degree are the computable ones, by Miller and Martin [18].…”

Section: Theorem 57 Each Low(cr) Set Is Computablementioning

confidence: 99%

Lowness properties and randomness

Nies

2005

Advances in Mathematics

174

286

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Section: Theorem 57 Each Low(cr) Set Is Computablementioning

confidence: 99%

Lowness properties and randomness

Nies

2005

Advances in Mathematics

174

286

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“…Hyperimmune-Free Degrees Martin and Miller in [Miller and Martin 1968] extended the definition of hyperimmune from a single set to an entire degree.…”

Section: 6mentioning

confidence: 99%

Turing Computability

Soare¹

2016

Theory and Applications of Computability

111

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CanadaFounding Editors: P. Bonizzoni, V. Brattka, S.B. Cooper, E. Mayordomo Books published in this series will be of interest to the research community and graduate students, with a unique focus on issues of computability. The perspective of the series is multidisciplinary, recapturing the spirit of Turing by linking theoretical and real-world concerns from computer science, mathematics, biology, physics, and the philosophy of science.The series includes research monographs, advanced and graduate texts, and books that offer an original and informative view of computability and computational paradigms.

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“…Following Miller and Martin [73], we say that A is hyperimmune-free iff for all functions f ≤ T A, there is a computable function g such that for all x, f (x) ≤ g(x).…”

Section: Theorem 336 (Nies Stephan and Terwijn [78]) Suppose That mentioning

confidence: 99%