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  • W. HUGH WOODIN (a1)

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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[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.
[3] Hamkins J. D., Extensions with the approximation and cover properties have no new large cardinals . Fundamenta Mathematicae, vol. 180 (2003), no. 3, pp. 257277.
[4] Jensen R., The fine structure of the constructible hierarchy . Annals of Mathematical Logic, vol. 4 (1972), pp. 229308.
[5] Jensen R., A new fine structure for higher core models, handwritten notes, 1990.
[6] Kanamori A., The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings, second ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.
[7] Kunen K., Some applications of iterated ultrapowers in set theory . Annals of Mathematical Logic, vol. 1 (1970), pp. 179227.
[8] Kunen K., Elementary embeddings and infinitary combinatorics . Journal of Symbolic Logic, vol. 36 (1971), pp. 407413.
[9] Magidor M., On the role of supercompact and extendible cardinals in logic . Israel Journal of Mathematics, vol. 10 (1971), pp. 147157.
[10] Martin D. A. and Steel J., A proof of projective determinacy . Journal of the American Mathematical Society, vol. 2 (1989), pp. 71125.
[11] Martin D. A. and Steel J., Iteration trees . Journal of the American Mathematical Society, vol. 7 (1994), pp. 174.
[12] Mitchell W. J. and Steel J. R., Fine Structure and Iteration Trees, Springer-Verlag, Berlin, 1994.
[13] Moschovakis Y. N., Descriptive Set Theory, North-Holland, Amsterdam, 1980.
[14] Neeman I., Inner models in the region of a Woodin limit of Woodin cardinals . Annals of Pure and Applied Logic, vol. 116 (2002), no. (1–3), pp. 67155.
[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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