# What does Sigma notation mean, in the context of computability of functions?

I was reading a paper on the computability of AIXI [1] and came across the notion of $\Sigma^0_n$-computability for real-valued functions in section 2.3.

I'd like to read about this in more detail. Unfortunately I couldn't find this definition anywhere else in the literature. I already checked the references given at the end of the paper.

Could somebody point me to some book/article I can take a look at?

1. On the Computability of AIXI by J. Leike and M. Hutter (2015)
• Can you pinpoint your difficulty? According to the paper, a function $f\colon \{0,1\}^* \to \mathbb{R}$ is in some class $C$ if the predicate $P(x,a,b) = [f(x) > a/b]$ is in the class $C$, where $x,a,b \in \{0,1\}^*$ and $a,b$ are interpreted as integers (and $b \neq 0$). – Yuval Filmus Sep 8 '16 at 18:43