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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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Are all mathematical theorems necessarily true?
Define a formal tautology as a statement where by the nature of its atomic components there exists no truth-value assignment where it is not true. A contingent statement is a statement that is true by …