Continuum hypothesis

What was discovered

The conjecture that there is no set of cardinality strictly between that of the naturals and that of the reals. The first problem on Hilbert's list and the prototype of a statement that turned out to be independent of the axioms.

Cantor tried to prove it for decades; it is now known that neither it nor its negation follows from ZFC.

What it led to

• Hilbert's first problem
• Gödel's relative consistency (1940)
• Cohen's forcing (1963)
• modern set theory and large cardinals

Built on

• Cantor's set theory

Made possible

• Hilbert 23 problems8 de agosto de 1900
• Forcing and independence of the continuum hypothesis1963

📄 Original publication

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