Work
He has done work on the theory of generic multiverses and related concept of Ω-logic which suggested an argument that the Continuum Hypothesis is either undecidable or false in the sense of Mathematical Platonism. Woodin criticizes this view arguing that it leads to a counterintuitive reduction in which all truths in the set theoretical universe can be decided from a small part of it. He claims that these and related mathematical results lead (intuitively) to the conclusion that Continuum Hypothesis has a truth value and the Platonistic approach is reasonable.
Woodin now predicts that there should be a way of constructing an inner model for almost all known large cardinals which he calls the Ultimate L and which would have similar properties as Gödel's constructible universe. In particular, the Continuum Hypothesis would be true in this universe.
Read more about this topic: W. Hugh Woodin
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