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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 …
manu fava's user avatar
  • 413
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. …
manu fava's user avatar
  • 413