10
votes
Accepted
Decidable properties of computable reals
Yes, Rice's theorem for reals holds in every reasonable version of computable reals.
I will first prove a certain theorem and a corollary, and explain what it has to do with computability later.
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8
votes
What is the "continuity" as a term in computable analysis?
Arno's answer provides some very useful background reading material, I would just like to address your specific question about $\mathbb{R}$.
Let us first recall a result by Peter Hertling, see Theorem ...
- 31.2k
8
votes
Accepted
What is the "continuity" as a term in computable analysis?
Different people have different views on what the definition of continuity should be, but the way I see it, we should define continuity to be computability relative to some oracle. For example:
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2
votes
What is the relationship between two definitions of Turing-computability of a partial function?
Definition 1 is incorrect. It does not define the notion of partial computable function correctly. Definition 2 is correct.
Proposition: A partial function $f$ is computable according to your ...
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1
vote
Accepted
What does Sigma notation mean, in the context of computability of functions?
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.
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