Linked from

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

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

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

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

• 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.

• 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.

• 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.

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

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