Abstract

This chapter discusses the concept of relative computability. The concept of relative computability first appeared in a 1939 paper by Alan Turing. At first glance, it might seem strange to combine the rather constructive concept of computability with the almost mystical idea of an oracle. It is to Turing's credit that he perceived that the combination, strange or not, would be a useful tool in classifying the noncomputable sets. The focus is on an informal description of the concept of effective calculability relative to a set. The plan is to make the concept into a genuine mathematical concept in two ways: general recursiveness relatives and register-machine computability relatives. Further, enumeration theorem and normal form theorem related to relative Computability is discussed followed by equivalence relations

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