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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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Is there a polynomial equation whose solution over the integers is independent of ZFC

Consider the algorithm that goes over all proofs in peano arithmetic. Allegedly, for a given multivariate polynomial equation we should find a proof or disproof of existence of an integer solution. Th …