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 knowledge of set theory is necessary.
To join this webinar, please send an email to r.zoghi@gmail.com.