We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. 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.
- Pub Date:
- August 2017
- Mathematics - Logic;
- Computer Science - Logic in Computer Science;
- Primary 03D65;
- Secondary 03C57;
- Logical Methods in Computer Science, Volume 15, Issue 2 (April 30, 2019) lmcs:5410