Algebra of sets Axiom of choice Axiom of countable choice Axiom of dependent choice Zorn's lemma Boolean algebra (structure) Boolean-valued model Burali-Forti paradox Cantor's back-and-forth method Cantor's diagonal argument Cantor's first uncountability proof Cantor's theorem Cantor–Bernstein–Schroeder theorem Cardinality Aleph number Aleph-null Aleph-one Beth number Cardinal number Hartogs number Cartesian product Class (set theory) Complement (set theory) Complete Boolean algebra Continuum (set theory) Suslin's problem Continuum hypothesis Countable set Descriptive set theory Analytic set Analytical hierarchy Borel equivalence relation Infinity-Borel set Lightface analytic game Perfect set property Polish space Prewellordering Projective set Property of Baire Uniformization (set theory) Universally measurable set Determinacy AD+ Axiom of determinacy Axiom of projective determinacy Axiom of real determinacy Empty set Forcing (mathematics) Fuzzy set Internal set theory Intersection (set theory) L L(R) Large cardinal property Musical set theory Ordinal number Infinite descending chain Limit ordinal Successor ordinal Transfinite induction ∈-induction Well-founded set Well-order Power set Russell's paradox Set theory Alternative set theory Axiomatic set theory Kripke–Platek set theory with urelements Morse–Kelley set theory Naive set theory New Foundations Positive set theory Zermelo–Fraenkel set theory Zermelo set theory Set (mathematics) Simple theorems in the algebra of sets Subset Θ (set theory) Tree (descriptive set theory) Tree (set theory) Union (set theory) Von Neumann universe Zero sharp