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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
Let me add to this long list the famous Nakayama lemma, a crucial result in commutative algebra, and whose original claim is as follows:
Let $(R,\mathfrak m)$ be a local ring and $M$ a finitely g …