The Continuum Hypothesis - Logic at Harvard

list of definite questions with the following features: First, the questions onthis list will have answers—independence is not an issue. Second, if the answersconverge then one will have strong evidence for new axioms settling theundecided statements (and hence non-pluralism about the universe of sets);whileiftheanswers oscillate, onewill haveevidence thatthese statements are“absolutely undecidable” and this will strengthen the case for pluralism. Inthis way the questions of “absolute undecidability” and pluralism are givenmathematical traction.Further Reading: For more on the structure theory of L(V λ+1 ) and the parallelwith determinacy see Woodin (Forthcoming).ReferencesAbraham, U. & Magidor, M. (2010). Cardinal arithmetic, (Foreman &Kanamori 2010), Springer.Bagaria,J., Castells, N.&Larson, P.(2006). AnΩ-logicprimer, inJ.Bagaria& S. Todorcevic (eds), Set theory, Trends in Mathematics, Birkhäuser,Basel, pp. 1–28.Foreman, M. & Kanamori, A. (2010). Handbook of Set Theory, Springer-Verlag.Foreman, M. & Magidor, M. (1995). Large cardinals and definable counterexamplesto the continuum hypothesis, Annals of Pure and AppliedLogic 76: 47–97.Foreman, M., Magidor, M. & Shelah, S. (1988). Martin’s Maximum, saturatedideals, and non-regular ultrafilters. Part i, Annals of Mathematics127: 1–47.Hallett, M. (1984). Cantorian Set Theory and Limitation of Size, Vol. 10 ofOxford Logic Guides, Oxford University Press.Holz, M., Steffens, K. & Weitz, E. (1999). Introduction to Cardinal Arithmetic,Birkhäuser Advanced Texts, Birkhäuser Verlag, Basel.Jech, T. J. (2003). Set Theory: Third Millennium Edition, Revised andExpanded, Springer-Verlag, Berlin.36