The Independence of the Continuum Hypothesis.

Cohen, P. J. (1963). The Independence of the Continuum Hypothesis. Proceedings of the National Academy of Sciences, 50(6), 1143-1148.

Type

Journal article

Intellectual base

Primary research

Year

1963

DOI

10.1073/pnas.50.6.1143

Link

https://doi.org/10.1073/pnas.50.6.1143

Cited from

mathematics

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Cardinality
  • … under the axiom of choice, indexed by the ordinals); uncountable cardinalities like $\mathfrak{c} = 2^{\aleph_0}$ (cardinality of $\mathbb{R}$) dominate $\aleph_0$ strictly; the Continuum Hypothesis ($\mathfrak{c} = \aleph_1$) is undecidable in ZFC (Gödel 1940 consistency, Cohen 1963 independence via forcing

    This sourceIntroduces forcing to prove ¬CH is consistent with ZFC; together with Gödel's L this establishes the independence of CH from ZFC.

• Infinity
  • and Cohen's (1963) forcing-based independence proof
• Set and Membership
  • Gödel's incompleteness theorems and his work on the consistency of the Continuum Hypothesis, combined with Cohen's forcing

Domain-specific

• Ramified forcing
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Verification

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://doi.org/10.1073/pnas.51.1.105 ×1

Registry ID ref:6825b19977bb · see in the full table