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IN SEARCH OF ULTIMATE-L THE 19TH MIDRASHA MATHEMATICAE LECTURES

  • W. HUGH WOODIN (a1)
Abstract

We give a fairly complete account which first shows that the solution to the inner model problem for one supercompact cardinal will yield an ultimate version of L and then shows that the various current approaches to inner model theory must be fundamentally altered to provide that solution.

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References
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[1] Feng, Q., Magidor, M., and Hugh Woodin, W., Universally Baire sets of reals , Set Theory of the Continuum (Judah, H., Just, W., and Woodin, H., editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer–Verlag, Heidelberg, 1992, pp. 203242.
[2] Foreman, M. and Magidor, M., A very weak square principle . Journal of Symbolic Logic, vol. 62 (1997), pp. 175198.
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[11] Martin, D. A. and Steel, J., Iteration trees . Journal of the American Mathematical Society, vol. 7 (1994), pp. 174.
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[15] Sargsyan, G., A tale of hybrid mice , Ph.D. thesis, U. C. Berkeley, 2009.
[16] Shelah, S., On successors of singular cardinals , Logic Colloquium ’78 (Mons, 1978) (Boffa, M., van Dalen, D., and McAloon, K., editors), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam-New York, 1979, pp. 357380.
[17] Solovay, R. M., The independence of DC from AD , Cabal Seminar 76–77 (Proceedings Caltech-UCLA Logic Seminar, 1976–77) (Kechris, A. S. and Moschovakis, Y. N., editors), Lecture Notes in Mathematics, vol. 689, Springer, Berlin, 1978, pp. 171183.
[18] Steel, J., Schindler, R., and Zeman, M., Deconstructing inner model theory . Journal of Symbolic Logic, vol. 67 (2002), pp. 712736.
[19] Usuba, T., The downward directed grounds hypothesis and very large cardinals, submitted, 2016.
[20] Hugh Woodin, W., Suitable extender models I . Journal of Mathematical Logic, vol. 10 (2010), no. 1–2, pp. 101341.
[21] Hugh Woodin, W., The Continuum Hypothesis, the generic-multiverse of sets, and the Ω Conjecture , Set Theory, Arithmetic and Foundations of Mathematics: Theorems, Philosophies (Kennedy, J. and Kossak, R., editors), Lecture Notes in Logic, vol. 36, Cambridge University Press, New York, NY, 2011, pp. 1342.
[22] Hugh Woodin, W., The weak Ultimate L Conjecture . Infinity, Computability, and Metamathematics (Geschke, S., Loewe, B., and Schlicht, P., editors), Tributes, vol. 23, College Publications, London, 2014, pp. 309329.
[23] Hugh Woodin, W., The axiom V = Ultimate-L, in preparation, 2016.
[24] Hugh Woodin, W., Fine structure at the finite levels of supercompactness, in preparation, 2016, 710 pp.
[25] Hugh Woodin, W., The Ultimate-L Conjecture, in preparation, 2016, 419 pp.
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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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