The $\Delta^0_\alpha$-computable enumerations of the classes of projective planes

Studying computable representations of projective planes, for the classes $K$ of pappian, desarguesian, and all projective planes, we prove that $K^c/_\simeq$ admits no hyperarithmetical Friedberg enumeration and admits a Friedberg $\Delta^0_{\alpha+3}$-computable enumeration up to a $\Delta^0_\alpha$-computable isomorphism.