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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 a paraconsistent and provably non-trivial foundation for math possible?
Would it be possible to use a paraconsistent logic and axioms similar to ZFC to create a formal sytem, that can be proven to be non-trivial (so that there are some statements which can´t be proven in …