  We prove that the theory of open projective planes is complete and strictly
stable, and infer from this that Marshall Hall's free projective planes $(\pi^n
: 4 \leq n \leq \omega)$ are all elementary equivalent and that their common
theory is strictly stable and decidable, being in fact the theory of open
projective planes. We further characterize the elementary substructure relation
in the class of open projective planes, and show in particular that $(\pi^n : 4
\leq n \leq \omega)$ is an elementary chain. We then prove that the theory of
open projective planes does not have a prime model, that it has elimination of
quantifiers down to Boolean combinations of existential formulas, and that it
is not model complete. Finally, we characterize the forking independence
relation in models of the theory and prove that the $\pi^n$'s ($4 \leq n \leq
\omega)$ are strongly type-homogeneous.

Logic