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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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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 …