Essentially the title.
Tarski's Euclidean geometry is complete. Is the same true of a theory of the real projective plane (as an example of a model of the theory I am interested in: take the extended Euclidean plane with opposing points at infinity identified)?
I don't have a reference for the real projective plane that considers this. Using von Staudt's throws (würfs) one can define a (maybe just a fragment of) arithmetic within the real projective plane. Is this arithmetic sufficiently strong such that Godel's incompleteness theorem applies?