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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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Does the "propositions-as-types" paradigm match mathematical practice?

Does the "propositions-as-type" paradigm matches mathematical practice? Or is logic in mathematical practice a layer beneath mathematics, and mathematics built on top? For example, should we distingui …