Ranked Forcing and the Length of Generalized Borel Hierarchies

Nick Chapman

We extend A. Miller's framework of $\hat{I}\pm$-forcing to the case of a regular uncountable cardinal $\hat{I}º=\hat{I}{º}^{<\hat{I}º}$ and apply it to study the structure of the $\hat{I}º$-Borel hierarchy on subs…