In my current work I am using facts 2.1.11 and 2.1.12 from Anand Pillay's book *Geometric Stability Theory*.


The facts are stated as follows:



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> *Fact 2.1.11*. Let $(S,\mbox{cl})$ be a locally projective, locally finite, infinite homogeneous geometry. Then $(S,\mbox{cl})$ is isomorphic to some affine or projective geometry over a finite field.
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and



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> *Fact 2.1.12*. If $(S,\mbox{cl})$ is a projective geometry of dimension at least 4, such that all $2$-dimensional closed sets have at least three elements, then $(S,\mbox{cl})$ is a projective geometry over some division ring.
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The author states this fact without reference, and I was not able to find one myself. Any directions would be very welcomed.



Looking for reference or proof to some facts stated on Anand Pillay's book
In the notes on chapters at the end of Geometric Stability Theory, I give references. For Fact 1.11 it is Doyen and Hubaut, Finite regular locally projective geometries, Math. Zeitschrift, 1971. 
Zilber's book, Uncountably categorical theories, Translations of Math. monographs, vol 117, AMS, 1993, also mentions this on p. 27.


