# Theorems in the foundations of mathematics This category includes theorems on the foundational aspects of mathematics, including: mathematical logic, model theory, set theory, some general topology and category theory. Theorems in the foundations of mathematics: * Banach-Tarski paradox * Barwise compactness theorem * Borel determinacy theorem * Bourbaki-Witt theorem * Cantor's diagonal argument * Cantor's theorem * Categorical theory * Church-Rosser theorem * Codd's theorem * Compactness theorem * Completeness of atomic initial sequents * Compression theorem * Craig's theorem * Cut-elimination theorem * Deduction theorem * Easton's theorem * Extension by new constant and function names * Frege's theorem * Gödel's speed-up theorem * Gödel's completeness theorem * Gödel's incompleteness theorems * Goodstein's theorem * Halpern-Läuchli theorem * Herbrand's theorem * Kanamori-McAloon theorem * Kleene's recursion theorem * Knaster-Tarski theorem * König's theorem (set theory) * Lindström's theorem * Löb's theorem * Löwenheim-Skolem theorem * Lusin's separation theorem * Paris-Harrington theorem * Post's theorem * Rice-Shapiro theorem * Rice's theorem * Richardson's theorem * Robinson's joint consistency theorem * Schröder-Bernstein theorem for measurable spaces * Schröder-Bernstein theorem * Szpilrajn extension theorem * Tarski's theorem about choice * Tennenbaum's theorem * Von Neumann paradox * Well-ordering theorem * Wilkie's theorem