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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)
D.W.
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Manlio
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2 Answers2

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Section 2.1 of that paper defines such computability for sets of natural numbers, and Section 2.3 of that paper then extends the notion to real-valued functions.

1

The key term for finding references is "arithmetical hierarchy of real numbers". In particular, the original article by Zheng and Weihrauch (correctly) defines those notions.

Manlio
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