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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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Impredicativity
I hope this question is not so elementary that it'll get me banned...
In mathematics we see a lot of impredicativity. Example of definitions involving impredicativity include: subgroup/ideal generate …