Random non-cupping revisited
نویسندگان
چکیده
منابع مشابه
Random non-cupping revisited
Say that Y has the strong random anticupping property if there is a set A such that for every Martin-Löf random set R
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We prove that a set is K-trivial if and only if it is not weakly ML-cuppable. Further, we show that a set below zero jump is K-trivial if and only if it is not ML-cuppable. These results settle a question of Kučera, who introduced both cuppability notions.
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Let Y ∈ ∆2 be Martin-Löf-random. Then there is a promptly simple set A such that for each Martin-Löf-random set Z, Y ≤T A ⊕ Z ⇒ Y ≤T Z. When Y = Ω, one obtains a c.e. non-computable set A which is not weakly Martin-Löf cuppable. That is, for any Martin-Löf-random set Z, if ∅′ ≤T A⊕ Z, then ∅′ ≤T Z.
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The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...
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We extend the notion of immunity to closed sets and to Π1 classes in particular in two ways: immunity meaning the corresponding tree has no infinite computable subset, and tree-immunity meaning it has no infinite computable subtree. We separate these notions from each other and that of being special, and show separating classes for computably inseparable c.e. sets are immune and perfect thin cl...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2006
ISSN: 0885-064X
DOI: 10.1016/j.jco.2006.03.007