The proof of the isomorphism of the \(n\)-dimensional projective spaces defined axiomatically (Q2716333)

The authors prove the following theorem: Any two projective spaces \(P_n\) and \(P_n'\) are isomorphic. The goal is the proof without using the ``great'' Desargues' axiom. NEWLINENEWLINENEWLINELet us recall that the projective space \(P_n\) of dimension \(n\geq 2\) is a non-empty set with \(n-1\) systems of non-empty subsets (so called subspaces) fulfilling the generalized Hilbert's axioms of incidence, the projective axiom and a special Desargues' axiom. NEWLINENEWLINENEWLINEThe isomorphism of projective spaces is a bijective mapping respecting subspaces and separation relations.