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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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Open problems in type theory
I am only a beginner in the field of type theory, and I'm wondering if the community could point me out a few open problems in the field. I have a good background in logic, in particular, proof theory …