Linked from

The 47 pages that link to Zermelo–Fraenkel set theory, each with the reason it gives.

• John von NeumannRelated: Von Neumann’s work helped shape the axiomatic approach later associated with this system.

• SetRelated: Its axioms replace unrestricted collection-building with controlled principles.

• Russell's paradoxRelated: Its axioms avoid unrestricted comprehension, preventing the Russell set from being formed.

• ParadoxRelated: Its axioms avoid the unrestricted set formation that produces Russell's paradox.

• Cantor's theoremRelated: Its power-set axiom ensures that every set has a power set to which the theorem applies.

• Universal quantificationRelated: Its axioms use quantifiers to state claims about all sets and their relationships.

• Cumulative hierarchyRelated: Its Foundation axiom formalizes the well-foundedness assumed by the hierarchy.

• Axiomatic methodRelated: Its axioms provide a widely used foundation in which many mathematical objects are defined.

• Axiom of extensionalityRelated: Extensionality is one of its standard axioms.

• Axiom of dependent choiceRelated: The axiom's independence and consequences are assessed relative to this foundational theory.

• Axiom schemaRelated: Its separation and replacement principles are specified by formula-indexed axiom families.

• Von Neumann universeRelated: Its axioms describe and constrain the sets in the hierarchy.

• Von Neumann–Bernays–Gödel set theoryRelated: NBG shares much of ZF’s set-theoretic foundation, while explicitly admitting proper classes.

• Skolem's paradoxRelated: Skolem's paradox concerns countable models of first-order set theories of this kind.

• Axiom of global choiceRelated: Its set-only language distinguishes ordinary choice from class-level global choice.

• Gödel's first incompleteness theoremRelated: If consistent, ZFC is incomplete by the theorem, as the continuum hypothesis shows.

• Mostowski collapse lemmaRelated: Its Foundation and Extensionality axioms clarify the lemma's hypotheses and interpretation.