SWhat changed
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.
Scientific scope
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. Scope limitation: 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.
Evidence
Assessment uses the catalogue-linked source evidence for the stated contribution. 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.
Contributors
- Paul J. Cohen · SCIENCE: Named source contributor; exact labor shares are not measured.
- Cohen, The Independence of the Continuum Hypothesis, PNAS 50(6), 1143–1148 (1963); Russian translation by A. G. Dragalin, Matematika 9(4), 142–148 (1965)
- Cohen, The Independence of the Continuum Hypothesis II, PNAS 51(1), 105–110 (1964); Russian translation, Matematika 9(4), 149–155 (1965)
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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