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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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Non-constructive proofs vs. efficient algorithms
Not a very serious answer, but maybe there is a little more than "how fast you can construct" to it when it comes to constructive proofs in some cases.
A typical combinatorial design is often describ …