Non-cupping and Randomness
نویسنده
چکیده
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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