IDENTIFYING NEARLY MINIMAL GODEL NUMBERS FROM ADDITIONAL INFORMATION

A new identification type close to the identification of minimal Godel numbers is considered. The type is defined by allowing as input both the graph of the target function and an arbitrary upper bound of the m inimal index of the target function in a Godel numbering of all partia l recursive functions. However, the result of the inference has to be bounded by a fixed function from the given bound. Results characterizi ng the dependence of this identification type from the underlying numb ering are obtained. In particular, it is shown that for a wide class o f Godel numberings, the class of all recursive functions can be identi fied even for small bounding functions.