The Continuum Hypothesis - Logic at Harvard

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Woodin, W. H. (2011a). The Continuum Hypothesis, the generic-multiverseofsets, andtheΩ-conjecture, inJ. Kennedy &R.Kossak(eds), Set Theory,Arithmetic, and Foundations of Mathematics: Theorems, Philosophies,Vol. 36 of Lecture Notes in Logic, Cambridge University Press.Woodin, W. H.(2011b). Suitableextender models I,Journal of MathematicalLogic 11(1–2): 101–339.Woodin, W.H.(Forthcoming). Suitableextender modelsII,Journal of MathematicalLogic .38
Page 1 and 2: The Continuum HypothesisPeter Koell
Page 3 and 4: and Determinacy”, which contains
Page 5 and 6: infinite cardinals: Assuming GCH, i
Page 7 and 8: Theorem 1.6 (Shelah, 1978). If ℵ
Page 9 and 10: this version of CH holds for all se
Page 11 and 12: more generally, all universally Bai
Page 13 and 14: arithmetic (orabout L(R)) inthepres
Page 15 and 16: 3.2 Ω-LogicWe will now recast the
Page 17 and 18: We will need a strong form of this
Page 19 and 20: and T A ≠ T B .How then shall one
Page 21 and 22: Now to arrive at this conclusion on
Page 23 and 24: Theorem 4.1 (Woodin). Assume ZFC an
Page 25 and 26: Theorem 4.6 (Woodin). Assume ZFC an
Page 27 and 28: forced to fail. The challenge for t
Page 29 and 30: So, of the various theories T A inv
Page 31 and 32: Theorem 5.8 (Koellner and Woodin).
Page 33 and 34: the fact that under (∗) the theor
Page 35 and 36: in his work.Now, we have a great de
Page 37: Koellner, P. (2010). Strong logics

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