The conventional wisdom presented in most computability books and historical papers is that there were several researchers
in the early 1930’s working on various precise definitions and demonstrations of a function specified by a finite procedure
and that they should all share approximately equal credit. This is incorrect. It was Turing alone who achieved the characterization, in the opinion of Gödel. We also explore Turing’s oracle machine and its analogous properties
in analysis.
Keywords Turing a-machine - computability - Church-Turing Thesis - Kurt Gödel - Alan Turing - Turing o-machine - computable approximations - effectively continuous functions on reals - computability in analysis - strong reducibilities reexamined