I have came accross the term "ambiguous class" in topology and I am surprised I have never seen any definition or introduction to it, or mentioning it together with Borel classes.
Ambiguous classes are mentioned for example in Engelen´s paper "Countable products of zero-dimensional absolute $F_{\sigma \delta}$ spaces" from 1984:
The next class in the Borel hierarchy is the ambiguous class 2, consisting of spaces which are both an absolute $F_{\sigma \delta}$ and an absolute $G_{\delta \sigma}$
So, does this mean that "ambiguous classes" are just "absolute Borel classes" of certain rank? (i.e. classes closed under countable unions and finite intersections etc. etc.) plus being absolute (i.e. having the property in every metrizable space in which it is embedded)?
I will be grateful for any comment/answer to this, also any resources for reading.