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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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Birkhoff's HSP theorem in categories other than $\mathbf{Set}$
Fix a category $C$ with finite products and a set $L$ of function symbols (each equipped with an arity in $\mathbb N$).
An $L$-algebra in $C$, $\mathbf A=(A,(f^\mathbf{A})_{f\in L})$, is given by some …