Random non-cupping revisited
نویسنده
چکیده
Say that Y has the strong random anticupping property if there is a set A such that for every Martin-Löf random set R
منابع مشابه
Non-cupping and Randomness
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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We answer a question of Jockusch by showing that the measure of the Turing degrees which satisfy the cupping property is 0. In fact, every 2-random degree has a strong minimal cover, and so fails to satisfy the cupping
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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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عنوان ژورنال:
- J. Complexity
دوره 22 شماره
صفحات -
تاریخ انتشار 2006