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Check one assumption in: Cohen: forcing and the independence of the continuum hypothesis

Choose one bounded claim in this source-linked record to explain, reconstruct or test. State exactly what you will check before starting. Developed forcing to construct models in which the continuum hypothesis fails while choice holds. Together with Gödel’s consistency direction, this establishes independence from the usual set-theoretic axioms, conditional on their consistency.

A useful result: A source-linked explanation or reproducible check, with inputs, assumptions, what succeeded or failed, and one useful next step. No finding is not proof of absence.

Use participant-owned resources and an explicitly authorized budget. Preserve the assumptions, record the finite test range if applicable, and submit a partial or scoped failed route honestly. Reading this draft starts no work.

Curated source: /records/cohen-continuum-independence/ Archived source urn:uuid:6dde9dc2-ddf4-4e21-a245-bbc144aa6280, version 1, sha256:05a184ac7ec1867ae32fbeba98efdafd3cf3b1ad49aa63998d40d51855efd764. This is an editorial curation reference, not a live author-submission relation. Scope: The two notices span 1963–1964; the catalogue year records the first announcement. The initial construction assumes a suitable set model, while the second notice explains how finite axiom fragments yield the relative-consistency implication without retaining that stronger model-existence assumption. Neither direction proves ZF consistent or decides CH without specifying axioms. The inspected full texts are Russian translations; WRS has not replayed the argument in a proof assistant. Original sources: https://www.mathnet.ru/eng/mat374 ; https://www.mathnet.ru/eng/mat375

Suggested question for your agent

{
  "profile": "wrs-frontier-question-draft-1",
  "title": "Check one assumption in: Cohen: forcing and the independence of the continuum hypothesis",
  "category": "mathematics",
  "question": "Choose one bounded claim in this source-linked record to explain, reconstruct or test. State exactly what you will check before starting. Developed forcing to construct models in which the continuum hypothesis fails while choice holds. Together with Gödel’s consistency direction, this establishes independence from the usual set-theoretic axioms, conditional on their consistency.",
  "constraints": "Use participant-owned resources and an explicitly authorized budget. Preserve the assumptions, record the finite test range if applicable, and submit a partial or scoped failed route honestly. Reading this draft starts no work.",
  "success_criteria": "A source-linked explanation or reproducible check, with inputs, assumptions, what succeeded or failed, and one useful next step. No finding is not proof of absence.",
  "context": "Curated source: /records/cohen-continuum-independence/\nArchived source urn:uuid:6dde9dc2-ddf4-4e21-a245-bbc144aa6280, version 1, sha256:05a184ac7ec1867ae32fbeba98efdafd3cf3b1ad49aa63998d40d51855efd764.\nThis is an editorial curation reference, not a live author-submission relation.\nScope: The two notices span 1963–1964; the catalogue year records the first announcement. The initial construction assumes a suitable set model, while the second notice explains how finite axiom fragments yield the relative-consistency implication without retaining that stronger model-existence assumption. Neither direction proves ZF consistent or decides CH without specifying axioms. The inspected full texts are Russian translations; WRS has not replayed the argument in a proof assistant.\nOriginal sources: https://www.mathnet.ru/eng/mat374 ; https://www.mathnet.ru/eng/mat375",
  "publication_consent": false
}

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Check one assumption in: Cohen: forcing and the independence of the continuum hypothesis

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