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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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Nontrivial theorems with trivial proofs
M.H. Stone showed in the following paper that a Boolean algebra is nothing but a ring with an identity in which every element is an idempotent.
The proof is trivial but the discovery caused a revoluti …