This is a linkpost for https://www.sciencedirect.com/science/article/pii/S0890540126000738
Admittedly haven't read in detail, but doesn't the arithmetic hierarchy already define real numbers via a bijection with P(N)? And the real numbers are themselves in bijections with the functions from N->R? Would the corresponding hierarchy of functions N->R be different than the hierarchy here?
I wrote a fairly accessible introduction to real hypercomputation with Marcus Hutter. The focus is on enabling applications to algorithmic information theory. This project was intended to build my technical foundations for studying AIXI, but took me a bit further afield and down some rabbit holes. In the future I will prefer to focus more tightly on AI safety.
Feedback would be appreciated. In particular, I needed to introduce an extra extensionality assumption for the real domain case, which I am still not sure is necessary.
Errata: The diagram of results currently has theorems misnumbered due to a typographical error.
Thanks to the LTFF for supporting my work over most of the research process.