Feedback computability on Cantor space - Nathanael L. Ackerman; Cameron E. Freer; Robert S. Lubarsky (Logical Methods in Computer Science, 2019)
We introduce the notion of feedback computable functions from $2^ω$ to $2^ω$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^ω$ to $2^ω$. We then show that the feedback computable functions are precisely the effectively Borel functions. With this as motivation we define the notion of a feedback computable function on a structure, independent of any coding of the structure as a real. We show that this notion is absolute, and as an example characterize those functions that are computable from a Gandy ordinal with some finite subset distinguished.