Can one solve the Continuum Hypothesis?
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Woodin has been an influential mathematician, and his opinions regarding CH have been widely discussed. Read below his popular account of his position. Unlike AC, the status of CH is complex, and therefore Woodin's argument is complex as well.
It is not necessary to understand all the technical details, just try to get some idea as to what a solution to CH should be like. Part I is easier to read, Part II is more technical. The paper also introduces the Axiom of Determinacy, which has been proposed as an alternative to AC.