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Thursday 4 March 2021   Today  
Events for day: Wednesday 03 February 2021    
           15:30 - 17:30     Mathtematical Logic Weekly Seminar
A Definable Hamel Basis without Choice


In 2016, Beriashvili, Wu, Yu, and the speaker answered a long standing open question by showing that in the Cohen-Halpern-Levy model (which has an infinite set of reals without a countable subset, in particular, there is no well-order of the reals) there is a Hamel basis, i.e., a basis for the reals construed as a vector space over the rationals. In later joint work with Kanovei, we produced a variant of this model in which choice fails as badly and in which there is a (lightface Delta^1_3) definable Hamel basis. We produce these results and state interesting open questions. The talk will be accessible to a broad audience, no specific knowle ...