Toward the end of his paper on the infinite Hilbert sketched his proof of the continuum hypothesis. [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1925)] Can experts on Hilbert give more details of his proof than are published there?
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4$\begingroup$ This question is already answered at length by Noah Schweber on Math Overflow, Hilbert's alleged proof of the Continuum Hypothesis in “On the Infinite” $\endgroup$– ConifoldFeb 21, 2018 at 20:25
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$\begingroup$ Very interesting. The elaborate work of Dreben and Kanamori reduces the probability to near zero that more of Hilbert's writings can be unearthed. $\endgroup$– Franz KurzFeb 22, 2018 at 8:28