Feedback computability on Cantor space
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 arXiv:
 arXiv:1708.01139
 Bibcode:
 2017arXiv170801139A
 Keywords:

 Mathematics  Logic;
 Computer Science  Logic in Computer Science;
 Primary 03D65;
 Secondary 03C57;
 03D30;
 03E15
 EPrint:
 Logical Methods in Computer Science, Volume 15, Issue 2 (April 30, 2019) lmcs:5410