Absolute $\mathcal F$-Borel classes
  We investigate and compare $\mathcal F$-Borel classes and absolute $\mathcal F$-Borel classes. We provide precise examples distinguishing these two hierarchies. We also show that for separable metrizable spaces, $\mathcal F$-Borel classes are automatically absolute. 
Vojt\v{e}ch Kova\v{r}\'ik
math.GN