A model with everything except for a well-ordering of the reals

Jörg Brendle, Fabiana Castiblanco, Ralf Schindler +2

We construct a model of $\mathsf{ZF}+\mathsf{DC}$ containing a Luzin set, a Sierpiński set, as well as a Burstin basis but in which there is no a well ordering of the continuum.