Theorems in the foundations of mathematics

https://en.wikipedia.org/wiki/Category: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