A Turing machine model for Kleene Type 2 recursion

We give an account of Kleene’s Type 2 recursion theory modelled on Turing machines. We apply this account to observe that the feedback computation of \cite{AFL2020} is an example of Kleene Recursion in ${}^2\mathsf{E}$. An application of Gandy Selection in the feedback setting solves questions there raised on uniformly finding indices for recursive unions {\em etc.} of feedback semi-computable sets; further it allows for effective choice and other principles.