Skip to main content
×
×
Home

DETERMINACY AND JÓNSSON CARDINALS IN L(ℝ)

  • S. JACKSON (a1), R. KETCHERSID, F. SCHLUTZENBERG (a2) and W. H. WOODIN (a3)
Abstract

Assume ZF + AD + V = L(ℝ) and let κ < Θ be an uncountable cardinal. We show that κ is Jónsson, and that if cof (κ) = ω then κ is Rowbottom. We also establish some other partition properties.

Copyright
References
Hide All
[1]Kanamori, Akihiro, The Higher Infinite: Large Cardinals in Set Theory from their Beginnings, second ed., Springer monographs in mathematics, Springer-Verlag, Berlin–New York, 2003.
[2]Kleinberg, E., Infinitary Combinatorics and the Axiom of Determinateness, vol. 612, Springer, Berlin–Heidelberg, 1977.
[3]Mitchell, William and Steel, John R., Fine Structure and Iteration Trees, Lectures Notes in Logic, vol. 3, Springer-Verlag, Berlin, 1994.
[4]Prikry, K., Changing measurable into accessible cardinals. Dissertationes Mathematicae (Rozprawy Matematyczne), vol. 68 (1970), pp. 552.
[5]Schlutzenberg, Farmer, Measures in mice, Ph.D. Thesis, University of California, Berkeley, 2007 arXiv:1301.4702.
[6]Schlutzenberg, Farmer, HODL(ℝ)is a core model below. The Bulletin of Symbolic Logic, vol. 1 (1995), no. 1, pp. 7584.
[7]Schlutzenberg, Farmer, An outline of inner model theory, Handbook of Set Theory (Matthew Foreman and Akihiro Kanamori, editors), vol. 3, Springer, Dordrecht, first ed., 2010.
[8]Steel, J. R., Woodin’s analysis of HODL(ℝ), unpublished notes available atwww.math.berkeley. edu/∼steel.
[9]Steel, J. R. and Woodin, W. H., HOD as a core model, Ordinal Definability and Recursion Theory, Volume III, The Cabal Seminar, to appear.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed