Israel Journal of Mathematics

, Volume 70, Issue 3, pp 381–394

Large cardinals imply that every reasonably definable set of reals is lebesgue measurable

  • Saharon Shelah
  • Hugh Woodin

DOI: 10.1007/BF02801471

Cite this article as:
Shelah, S. & Woodin, H. Israel J. Math. (1990) 70: 381. doi:10.1007/BF02801471


We prove that if there is a supercompact cardinal or much smaller large cardinals, then every set of reals from L(R) is Lebesgue measurable, and similar results. We also introduce some large cardinals.

Copyright information

© The Weizmann Science Press of Israel 1990

Authors and Affiliations

  • Saharon Shelah
    • 1
    • 3
  • Hugh Woodin
    • 2
    • 3
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA