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.

• Set theoryBroader topic: Its axioms form the standard framework for much contemporary foundational mathematics.

• Axiom of choiceNarrower topic: The axiom of choice is studied as an addition to this foundational theory.

• Georg CantorBroader topic: Modern set theory formalizes the mathematical universe Cantor helped create.

• Continuum hypothesisNarrower topic: The continuum hypothesis is studied for its consequences relative to these axioms.

• 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.

• Well-ordering theoremNarrower topic: The theorem's equivalence to choice is stated relative to this set-theoretic framework.

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

• Ernst ZermeloBroader topic: Zermelo’s 1908 axioms were the starting point for this later, expanded foundation.

• 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 of pairingNarrower topic: Pairing is one of its standard axioms.

• Infinite setNarrower topic: Its axioms specify which infinite sets can be formed and how they behave.

• Axiom of FoundationNarrower topic: Foundation is one of the axioms in this standard theory.

• Forcing (mathematics)Narrower topic: Forcing studies extensions of models of this theory, usually in its ZFC form.

• Gödel's constructible universeNarrower topic: Gödel’s relative consistency results take this set theory as their base.

• Peano axiomsCompared with: It can construct the natural numbers as sets rather than taking them as primitive objects.

• Axiom of constructibilityNarrower topic: The consistency claim concerns extending this theory by V = L.

• Axiom of infinityNarrower topic: The axiom of infinity is one of its standard existence axioms.

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

• Axiom schema of specificationBroader topic: ZF includes specification as a schema, with one axiom for each formula.

• Axiomatic systemBroader topic: Its independence results provide prominent examples of limits on what axioms determine.

• Membership relationNarrower topic: Its axioms constrain how membership can form sets and how sets relate.

• Axiom of Power SetNarrower topic: Power Set is one of its standard axioms.

• Martin's axiomNarrower topic: Martin's axiom is an additional principle considered over this foundational background.

• Axiom of countable choiceNarrower topic: Countable choice is studied as an additional axiom over this choice-free foundation.

• Large cardinalNarrower topic: Large-cardinal existence is typically studied as an additional axiom over this foundation.

• 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.

• New FoundationsCompared with: Unlike New Foundations, it does not admit a universal set.

• Aleph numberNarrower topic: Aleph arithmetic is studied within this foundational framework, usually with choice added.

• Axiom of regularityNarrower topic: Regularity is one of its standard axioms.

• Axiom schema of replacementNarrower topic: Replacement is one of the axioms distinguishing ZF from weaker set theories.

• Well-orderNarrower topic: The equivalence between choice and well-ordering is stated within this foundational framework.

• Axiom (general principle)Broader topic: Its axioms provide a widely used foundation for modern mathematics.

• Axiom of Empty SetNarrower topic: The axiom is one of its standard existence assumptions.

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

• Axiom (mathematics and logic)Broader topic: Its axioms provide a widely used foundation for much of modern mathematics.

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

• Borel conjectureNarrower topic: The conjecture’s independence is assessed relative to this standard foundation.

• 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.