The theory of projective planes is complete with respect to degree spectra and effective dimensions

We prove that the theory of Pappian projective planes is complete with respect to degree spectra of automorphically nontrivial structures, effective dimensions, degree spectra of relations, categoricity spectra, and automorphism spectra. Therefore, for every natural $n\ge2$, there exists a computable Pappian projective plane with computable dimension $n$.