Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-22T14:23:06.240Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  03 April 2017

W. HUGH WOODIN*
Affiliation:
DEPARTMENT OF MATHEMATICS DEPARTMENT OF PHILOSOPHY HARVARD UNIVERSITY CAMBRIDGE, MA, 02138, USAE-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

Type
Article
Copyright
Copyright © The Association for Symbolic Logic 2017 

References

REFERENCES

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.CrossRefGoogle Scholar
Foreman, M. and Magidor, M., A very weak square principle . Journal of Symbolic Logic, vol. 62 (1997), pp. 175198.CrossRefGoogle Scholar
Hamkins, J. D., Extensions with the approximation and cover properties have no new large cardinals . Fundamenta Mathematicae, vol. 180 (2003), no. 3, pp. 257277.CrossRefGoogle Scholar
Jensen, R., The fine structure of the constructible hierarchy . Annals of Mathematical Logic, vol. 4 (1972), pp. 229308.CrossRefGoogle Scholar
Jensen, R., A new fine structure for higher core models, handwritten notes, 1990.Google Scholar
Kanamori, A., The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings, second ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Google Scholar
Kunen, K., Some applications of iterated ultrapowers in set theory . Annals of Mathematical Logic, vol. 1 (1970), pp. 179227.CrossRefGoogle Scholar
Kunen, K., Elementary embeddings and infinitary combinatorics . Journal of Symbolic Logic, vol. 36 (1971), pp. 407413.CrossRefGoogle Scholar
Magidor, M., On the role of supercompact and extendible cardinals in logic . Israel Journal of Mathematics, vol. 10 (1971), pp. 147157.CrossRefGoogle Scholar
Martin, D. A. and Steel, J., A proof of projective determinacy . Journal of the American Mathematical Society, vol. 2 (1989), pp. 71125.CrossRefGoogle Scholar
Martin, D. A. and Steel, J., Iteration trees . Journal of the American Mathematical Society, vol. 7 (1994), pp. 174.CrossRefGoogle Scholar
Mitchell, W. J. and Steel, J. R., Fine Structure and Iteration Trees, Springer-Verlag, Berlin, 1994.CrossRefGoogle Scholar
Moschovakis, Y. N., Descriptive Set Theory, North-Holland, Amsterdam, 1980.Google Scholar
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.CrossRefGoogle Scholar
Sargsyan, G., A tale of hybrid mice , Ph.D. thesis, U. C. Berkeley, 2009.Google Scholar
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.Google Scholar
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.Google Scholar
Steel, J., Schindler, R., and Zeman, M., Deconstructing inner model theory . Journal of Symbolic Logic, vol. 67 (2002), pp. 712736.Google Scholar
Usuba, T., The downward directed grounds hypothesis and very large cardinals, submitted, 2016.CrossRefGoogle Scholar
Hugh Woodin, W., Suitable extender models I . Journal of Mathematical Logic, vol. 10 (2010), no. 1–2, pp. 101341.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
Hugh Woodin, W., The axiom V = Ultimate-L, in preparation, 2016.Google Scholar
Hugh Woodin, W., Fine structure at the finite levels of supercompactness, in preparation, 2016, 710 pp.Google Scholar
Hugh Woodin, W., The Ultimate-L Conjecture, in preparation, 2016, 419 pp.Google Scholar