▁cover ▁that ▁does ▁not ▁contain ▁S ; ▁this ▁property ▁can ▁be ▁seen ▁to ▁be ▁defin able ▁by ▁a ▁ ▁formula . ▁ ▁There ▁is ▁a ▁random ▁sequence ▁which ▁is ▁, ▁that ▁is , ▁comput able ▁relative ▁to ▁an ▁oracle ▁for ▁the ▁Hal ting ▁problem . ▁( S chn orr ▁ 1 9 7 1 ) ▁ ▁Ch ait in ' s ▁ Ω ▁is ▁an ▁example ▁of ▁such ▁a ▁sequence . ▁ ▁No ▁random ▁sequence ▁is ▁decid able , ▁comput ably ▁enumer able , ▁or ▁co - comput ably - en umer able . ▁Since ▁these ▁correspond ▁to ▁the ▁, ▁, ▁and ▁ ▁levels ▁of ▁the ▁ar ithmet ical ▁hierarchy , ▁this ▁means ▁that ▁ ▁is ▁the ▁lowest ▁level ▁in ▁the ▁ar ithmet ical ▁hierarchy ▁where ▁random ▁sequences ▁can ▁be ▁found . ▁ ▁Every ▁sequence ▁is ▁T uring ▁redu cible ▁to ▁some ▁random ▁sequence . ▁( K u č era ▁ 1 9 8 5 / 1 9 8 9 , ▁G á cs ▁ 1 9 8 6 ). ▁ ▁Thus ▁there ▁are ▁random ▁sequences ▁of ▁arbitr arily ▁high ▁T uring ▁degree . ▁▁ ▁Rel ative ▁random ness ▁ ▁As ▁each ▁of ▁the ▁equivalent ▁definitions ▁of ▁a ▁Martin - L ö f ▁random ▁sequence ▁is ▁based ▁on ▁what ▁is ▁comput able ▁by ▁some ▁T uring ▁machine , ▁one ▁can ▁naturally ▁ask ▁what ▁is ▁comput able ▁by ▁a ▁T uring ▁oracle ▁machine . ▁For ▁a ▁fixed ▁oracle ▁A , ▁a ▁sequence ▁B ▁which ▁is ▁not ▁only ▁random ▁but ▁in ▁fact , ▁satisfies ▁the