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A mathematical proof of S. Shelah’s theorem on the measure problem and related results

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Abstract

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,K σ-regularity and Ramsey property.

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Authors and Affiliations

  1. UER 47, Université Paris VI, 4, Place Jussieu, 75230, Paris Cedex 05, France

    Jean Raisonnier

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  1. Jean Raisonnier
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Raisonnier, J. A mathematical proof of S. Shelah’s theorem on the measure problem and related results. Israel J. Math. 48, 48–56 (1984). https://doi.org/10.1007/BF02760523

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  • DOI: https://doi.org/10.1007/BF02760523

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