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The 32 pages that link to Continuum hypothesis, each with the reason it gives.

• Set theoryRelated: Its independence from the standard axioms illustrates limits on what those axioms determine.

• Gödel's incompleteness theoremsRelated: Gödel and Cohen proved its independence, an incompleteness phenomenon made concrete.

• Zermelo–Fraenkel set theoryBroader topic: Its independence from ZF illustrates limits on what the axioms determine.

• Georg CantorRelated: Cantor investigated whether the first uncountable cardinal is the continuum’s size.

• CardinalityRelated: It asks whether the first two familiar infinite sizes have an intermediate cardinality.

• Countable setRelated: It asks how the first uncountable size relates to countable infinity.

• Kurt GödelRelated: Gödel proved it consistent with the standard axioms of set theory, given those axioms are consistent.

• Cantor's theoremRelated: Cantor’s theorem guarantees larger cardinalities but does not settle this proposed gap.

• Cantor's diagonal argumentRelated: The proof establishes the continuum’s uncountability but does not settle this hypothesis.

• Cardinal numberRelated: It asks whether the continuum is the next cardinal after countable infinity.

• Independence (mathematical logic)Broader topic: It is independent of the usual Zermelo–Fraenkel set theory with choice, if that theory is consistent.

• Infinite setRelated: It asks whether the smallest uncountable infinity is the continuum's only possible intermediate size.

• Wacław SierpińskiRelated: Sierpiński investigated the hypothesis and its connections to set theory and the axiom of choice.

• Descriptive set theoryCompared with: Its independence illustrates how set-theoretic assumptions can alter the surrounding theory.

• Forcing (mathematics)Related: Forcing helped show that this hypothesis cannot be decided from ZFC, assuming ZFC is consistent.

• Gödel's constructible universeBroader topic: The generalized continuum hypothesis in L includes this famous special case.

• InfinityRelated: Its independence from standard set theory shows limits on what axioms determine about infinity.

• Uncountable setRelated: It asks whether the real numbers are the smallest uncountable set in cardinality.

• Axiom of constructibilityRelated: Gödel’s constructible universe proof showed that CH holds in a model of ZF.

• Axiom of Power SetRelated: Power-set cardinality connects the hypothesis to the size of the power set of the natural numbers.

• Eleatic schoolRelated: Zeno’s distance paradoxes made the structure of continuous magnitude a lasting problem.

• Martin's axiomCompared with: Its status changes how many dense sets Martin's axiom permits.

• Hilbert's problemsBroader topic: Hilbert's first problem asks whether this hypothesis follows from accepted set-theoretic axioms.

• Zeno's paradoxesRelated: It illustrates how modern mathematics distinguishes different sizes of infinity, beyond Zeno's original problems.

• Number (mathematics)Related: It asks whether the infinite sizes of two fundamental number systems have an intermediate size.

• Aleph numberRelated: It asserts that the continuum has cardinality ℵ₁.

• Solovay modelRelated: Solovay’s work grew from the independence landscape shaped by forcing and continuum questions.

• Cardinality of the continuumRelated: It asks whether 𝔠 is exactly the next cardinal after ℵ₀.

• Axiom (mathematics and logic)Related: It is independent of the standard Zermelo–Fraenkel axioms with the axiom of choice, assuming consistency.

• Borel conjectureCompared with: Unlike this cardinality assertion, the Borel conjecture restricts sets by a covering property.

• Gödel's first incompleteness theoremRelated: Independence from ZFC, via Gödel and Cohen, extends incompleteness beyond arithmetic.

• Mary Ellen RudinRelated: Set-theoretic assumptions such as this shape questions about topological examples.