Computable dimensions of Pappusian and Desarguesian projective planes

Computable presentations of projective planes are studied. Based on an interpretation of a class of fields (associative skew fields) within a class of Pappusian (Desarguesian) projective planes, it is proved that the question whether there exists a computable presentation for a Pappusian (Desarguesian) projective plane reduces to asking if there exists a computable presentation for a corresponding field (associative skew field). It is stated that the computable dimension of a Pappusian (Desarguesian) projective plane coincides with that of a corresponding field (associative skew field).