Hyperarithmetictheoryisthefirststepbeyondclassicalrecursiontheory.Itistheprimarysourceofideasandexamplesinhigherrecursiontheory.Itisalsoacrossroadforseveralareasofmathematicallogic:insettheoryitisaninitialsegmentofGodel'sL;inmodeltheory,theleastadmissiblesetafter;indescript