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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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Translate ZFC statements into systems of Diophantine equations compatibly with geometry
For any ZFC statement we can build a Turing machine that enumerates all proofs in ZFC and halts if and when it finds a proof of the statement. Then we can find a system of Diophantine equations that h …