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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.

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Description of all total recursive functions where operator is effective?

What is a description of all total recursive functions $g(x)$ for which the operator$$\Phi_g: \mathcal{F}_2 \to \mathcal{F}_1$$defined by the formula$$\Phi_g(f)(x) := g(\mu y(f(x, y) = 0))$$is effecti …
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