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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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What if Current Foundations of Mathematics are Inconsistent?
The inconsistency of mathematics is a quite common option when you consider seriously some non-classical logics.
For an introduction, read the following page from the Stanford Encyclopedia of Philos …