[Settfa] Tuesday 16/04, Ralf Schindler

[kubis at math.cas.cz]

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 Tuesday 16th April, 10:00am 
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 Speaker:Ralf Schindler, University of Münster
 Title: Paradoxical sets with no well-ordering of the reals

 Abstract  

 By a Hamel basis we mean a basis for the reals, R, construed as a vecor space over the field of rationals. In 1905, G. Hamel constructed such a basis from a well-ordering of R. In 1975, D. Pincus and K. Prikry asked "whether a Hamel basis exists in any model in which R cannot be well ordered." About two years ago, we answered this positively in a joint paper with M. Beriashvili, L. Wu, and L. Yu. In more recent joint work, additionally with J. Brendle and F. Castiblanco we constructed a model of ZF with a Luzin set, a Sierpi?ski set, a Burstin basis, and a Mazurkiewicz set, but with no well-ordering of R. In joint work with V. Kanovei, we constructed such a model in which even (almost) all those "paradoxical" sets are projective.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .