There is a claim on https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines that 'Simple inductive Turing machines are equivalent to other models of computation such as general Turing machines of Schmidhuber, trial and error predicates of Hilary Putnam, limiting partial recursive functions of Gold, and trial-and-error machines of Hintikka and Mutanen.[1] More advanced inductive Turing machines are much more powerful. There are hierarchies of inductive Turing machines that can decide membership in arbitrary sets of the arithmetical hierarchy'. 

Are inductive turing machines different from turing machines with oracles?

Are inductive turing machines physically realizable?

Can inductive turing machines solve the halting problem (in essence Hilbert's $10$th as well)?