A mathematical proof of S. Shelah’s theorem on the measure problem and related results |
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Authors: | Jean Raisonnier |
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Institution: | (1) UER 47, Université Paris VI, 4, Place Jussieu, 75230 Paris Cedex 05, France |
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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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Keywords: | |
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