Journal of Symbolic Logic

$K$ without the measurable

Ronald Jensen and John Steel

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Abstract

We show in ZFC that if there is no proper class inner model with a Woodin cardinal, then there is an absolutely definable core model that is close to $V$ in various ways.

Article information

Source
J. Symbolic Logic, Volume 78, Issue 3 (2013), 708-734.

Dates
First available in Project Euclid: 6 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1389032272

Digital Object Identifier
doi:10.2178/jsl.7803020

Mathematical Reviews number (MathSciNet)
MR3135495

Zentralblatt MATH identifier
1348.03049

Citation

Jensen, Ronald; Steel, John. $K$ without the measurable. J. Symbolic Logic 78 (2013), no. 3, 708--734. doi:10.2178/jsl.7803020. https://projecteuclid.org/euclid.jsl/1389032272


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References

  • K. J. Devlin and R. B. Jensen Marginalia to a theorem of Silver, Proceedings of the ISILC logic conference (G. H. Müller, A. Oberschelp, and K. Potthoff, editors), Springer Lecture Notes in Mathematics, vol. 499, Springer, Berlin,1975, pp. 115–142.
  • A. J. Dodd and R. B. Jensen The core model, Annals of Mathematical Logic, vol. 20(1981), pp. 43–75.
  • –––– The covering lemma for $K$, Annals of Mathematical Logic, vol. 22(1982), pp. 1–30.
  • –––– The covering lemma for $L[U]$, Annals of Mathematical Logic, vol. 22(1982), pp. 127–135.
  • Gunter Fuchs $\lambda$-structures and $s$-structures: translating the models, Annals of Pure and Applied Logic, vol. 162(2011), pp. 257–317.
  • M. Gitik, R. Schindler, and S. Shelah Pcf theory and Woodin cardinals, Logic Colloquium '02, Lecture Notes in Logic, vol. 27, Association for Symbolic Logic, Urbana IL,2006, pp. 172–205.
  • R. B. Jensen The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4(1972), pp. 229–308.
  • –––– Robust extenders, handwritten notes,2003, family www.mathematik.hu-berlin.de/\~raesch/org/jensen.html.
  • –––– A new fine structure, handwritten notes, family www.mathematik.hu-berlin.de/\~raesch/org/jensen.html.
  • R. B. Jensen, E. Schimmerling, R. D. Schindler, and J. R. Steel Stacking mice, Journal of Symbolic Logic, vol. 74(2009), pp. 315–335.
  • W. J. Mitchell The core model for sequences of measures II, unpublished preliminary draft,1982.
  • –––– The core model for sequences of measures I, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 95(1984), pp. 229–260.
  • W. J. Mitchell and E. Schimmerling Weak covering without countable closure, Mathematical Research Letters, vol. 2(1995), no. 5, pp. 595–609.
  • W. J. Mitchell, E. Schimmerling, and J. R. Steel The covering lemma up to a Woodin cardinal, Annals of Pure and Applied Logic, vol. 84(1997), pp. 219–255.
  • W. J. Mitchell and R. D. Schindler A universal extender model without large cardinals in $V$, Journal of Symbolic Logic, vol. 69(2004), pp. 371–386.
  • W. J. Mitchell and J. R. Steel Fine structure and iteration trees, Lecture Notes in Logic, vol. 3, Springer-Verlag,1994.
  • E. Schimmerling and J. R. Steel The maximality of the core model, Transactions of the American Mathematical Society, vol. 351(1999), no. 8, pp. 3119–3141.
  • E. Schimmerling and M. Zeman Square in core models, Bulletin of Symbolic Logic, vol. 7(2001), pp. 305–314.
  • –––– Characterization of $\square_\kappa$ in core models, Journal of Mathematical Logic, vol. 4(2004), pp. 1–72.
  • R. D. Schindler The core model for almost linear iterations, Annals of Pure and Applied Logic, vol. 116(2002), pp. 207–274.
  • F. Schlutzenberg Measures in mice, Ph.D. thesis, University of California at Berkeley,2007.
  • J. R. Steel The core model iterability problem, Lecture Notes in Logic, vol. 8, Springer-Verlag,1996.
  • –––– $\textsf{{PFA}}$ implies $\ad$ in $L(\mathbb{R})$, Journal of Symbolic Logic, vol. 70(2005), no. 4, pp. 1255–1296.
  • –––– Derived models associated to mice, Computational prospects of infinity (C. T. Chong, Q. Feng, T. A. Slaman, and W. H. Woodin, editors), World Scientific,2008, pp. 105–193.
  • –––– An outline of inner model theory, Handbook of set theory (M. Foreman and A. Kanamori, editors), vol. 3, Springer,2010, pp. 1595–1684.