ö f ▁random ness ▁ ▁Rel ative ▁random ness ▁gives ▁us ▁the ▁first ▁notion ▁which ▁is ▁stronger ▁than ▁Martin - L ö f ▁random ness , ▁which ▁is ▁random ness ▁relative ▁to ▁some ▁fixed ▁oracle ▁A . ▁For ▁any ▁oracle , ▁this ▁is ▁at ▁least ▁as ▁strong , ▁and ▁for ▁most ▁or acles , ▁it ▁is ▁strictly ▁stronger , ▁since ▁there ▁will ▁be ▁Martin - L ö f ▁random ▁sequences ▁which ▁are ▁not ▁random ▁relative ▁to ▁the ▁oracle ▁A . ▁Import ant ▁or acles ▁often ▁considered ▁are ▁the ▁hal ting ▁problem , ▁, ▁and ▁the ▁n th ▁jump ▁oracle , ▁, ▁as ▁these ▁or acles ▁are ▁able ▁to ▁answer ▁specific ▁questions ▁which ▁naturally ▁arise . ▁A ▁sequence ▁which ▁is ▁random ▁relative ▁to ▁the ▁oracle ▁ ▁is ▁called ▁n - random ; ▁a ▁sequence ▁is ▁ 1 - random , ▁therefore , ▁if ▁and ▁only ▁if ▁it ▁is ▁Martin - L ö f ▁random . ▁A ▁sequence ▁which ▁is ▁n - random ▁for ▁every ▁n ▁is ▁called ▁ar ithmet ically ▁random . ▁The ▁n '' - random ▁sequences ▁sometimes ▁arise ▁when ▁considering ▁more ▁complicated ▁properties . ▁For ▁example , ▁there ▁are ▁only ▁count ably ▁many ▁ ▁sets , ▁so ▁one ▁might ▁think ▁that ▁these ▁should ▁be ▁non - random . ▁However , ▁the ▁hal ting ▁probability ▁ Ω ▁is ▁ ▁and ▁ 1 - random ; ▁it ▁is ▁only ▁after ▁ 2 - random ness ▁is ▁reached ▁that ▁it ▁is ▁impossible ▁for ▁a ▁random ▁set ▁to ▁be ▁. ▁ ▁We aker ▁than ▁Martin -