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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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votes
Pressure to defend the relevance of one's area of mathematics
Just point at our current high-technological society and say:
None of this would be possible without extensive work on mathematics.
And at that point in time they had no idea just exactly which bra …