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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
2
votes
0
answers
163
views
f(f(x)) computable but f(f(f(x))) not computable
Like the title says, I am looking for a function f from N to N such that f(f(x)) is computable but f(f(f(x))) is not. I think it should exist, because i dont see how knowing how to calculate f(f(x)) w …
29
votes
3
answers
4k
views
"Natural" undecidable problems not reducible to the halting problem
There is a lot of known examples of undecidable problems, a large amount of them not directly related to turing machines or equivalent models of computations, for example here: https://en.m.wikipedia. …