CDMTCS Research Report Series Higher Randomness Notions and Their Lowness Properties
نویسندگان
چکیده
We study randomness notions given by higher recursion theory, establishing the relationships Π1-randomness ⊂ Π1-Martin-Löf randomness ⊂ ∆1randomness = ∆1-Martin-Löf randomness. We characterize the set of reals that are low for ∆1 randomness as precisely those that are ∆1 -traceable. We prove that there is a perfect set of such reals.
منابع مشابه
Higher Randomness Notions and Their Lowness Properties
We study randomness notions given by higher recursion theory, establishing the relationships Π1-randomness ⊂ Π1-Martin-Löf randomness ⊂ ∆1randomness = ∆1-Martin-Löf randomness. We characterize the set of reals that are low for ∆1 randomness as precisely those that are ∆ 1 1 -traceable. We prove that there is a perfect set of such reals.
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1 Computability and randomness 1 1.1 Studying randomness notions . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Martin-Löf’s randomness notion . . . . . . . . . . . . . . . . . 2 1.1.2 Notions weaker than ML-randomness . . . . . . . . . . . . . . 2 1.1.3 A notion stronger than ML-randomness . . . . . . . . . . . . . 3 1.2 Lowness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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تاریخ انتشار 2007