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We observe that Hall's free projective extension $P \mapsto F(P)$ of partialplanes is a Borel map, and use a modification of the construction introduced in[9] to conclude that the class of countable non-Desarguesian projective planesis Borel complete. In the process, we also rediscover the main result of [7] onthe realizability of every group as the group of collineations of someprojective plane. Finally, we use classical results of projective geometry toprove that the class of countable Pappian projective planes is Borel complete.

The Class of Countable Projective Planes is Borel Complete