σ-fields of bad Borel sets

A “bad Borel subfield” of a space X is an infinite countably σ-generated σ-subfield of Borel sets none of which (other than Ø and X) is open or closed. X has “very bad Borel subfields” if, for each countable ordinal α, there is such a field of Borel sets none of which (other than Ø and X) is of Borel class less than α. Under suitable conditions on X, such fields are constructed, and a possible alternative construction is discussed.