Internal descriptions of absolute Borel classes

We present internal descriptions of spaces of absolute Borel classes with respect to Tychonoff spaces. Complete sequences of covers is the basic tool for this description. We apply the same technique to a hierarchy of absolute classes of scattered-Borel sets, covering thus the case of a hierarchy of extended Borel sets in nonseparable metrizable spaces which was introduced and studied by Hansell. We discuss briefly preservation of (extended) Borel classes both by open continuous and by perfect maps.