Recently, S. Shelah proved that an inaccessible cardinal is necessary to build a model of set theory in which every set of reals is Lebesgue measurable. We give a simpler and metamathematically free proof of Shelah's result. As a corollary, we get an elementary proof of the following result (without choice axiom): assume there exists an uncountable well ordered set of reals, then there exists a non-measurable set of reals. We also get results about Baire property, Kσ-regularity and Ramsey property. © 1984 Hebrew University.
CITATION STYLE
Raisonnier, J. (1984). A mathematical proof of S. Shelah’s theorem on the measure problem and related results. Israel Journal of Mathematics, 48(1), 48–56. https://doi.org/10.1007/BF02760523
Mendeley helps you to discover research relevant for your work.