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      "statement": "# Cohen: forcing and the independence of the continuum hypothesis\n\nDeveloped 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.\n\n## Scientific scope\n\nThe 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.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nPaul J. Cohen\n\nListed source contributors; individual labor shares are not measured\n\n\n\n## Original sources\n\n- [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)](https://www.mathnet.ru/eng/mat374)\n- [Cohen, The Independence of the Continuum Hypothesis II, PNAS 51(1), 105–110 (1964); Russian translation, Matematika 9(4), 149–155 (1965)](https://www.mathnet.ru/eng/mat375)\n",
      "summary": "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.",
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