The arithmetic hierarchy of real functions

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. Discuss