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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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Computability of sets of fixed point values
Recall that Rogers' fixed point theorem states that, if $f$ is a total computable function, then it has a fixed point value, i.e., there is an index $i$ such that $\varphi_i\simeq\varphi_{f(i)}$.
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