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Foundations of mathematics

Table of contents

Theorems in the foundations of mathematics

Lemmas in set theory

Condensation lemma

Fodor's lemma

Moschovakis coding lemma

Mostowski collapse lemma

Rasiowa–Sikorski lemma

Zorn's lemma

Barwise compactness theorem

Borel determinacy theorem

Bourbaki–Witt theorem

Codd's theorem

Completeness of atomic initial sequents

Craig's theorem

Cut-elimination theorem

Deduction theorem

Extension by new constant and function names

Frege's theorem

Gödel's speed-up theorem

Herbrand's theorem

Kanamori–McAloon theorem

Kleene's recursion theorem

Knaster–Tarski theorem

Lindström's theorem

Lusin's separation theorem

Löb's theorem

Paris–Harrington theorem

Post's theorem

Rice's theorem

Rice–Shapiro theorem

Richardson's theorem

Robinson's joint consistency theorem

Schröder–Bernstein theorem for measurable spaces

Szpilrajn extension theorem

Tarski's undefinability theorem

Well-ordering theorem

Axiom of reducibility

Dependent type

Multiverse (set theory)

Relationship between mathematics and physics

Univalent foundations

Zermelo–Fraenkel set theory

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