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 == Desarguesian spaces == 

 I reverted the good faith edit which stated that Galois geometries are usually called finite Desarguesian spaces. This is not a true statement. Only in two dimensions is there a need to distinguish Desarguesian planes from other projective planes. As soon as the dimension gets to be three or more Desargues theorem is automatic and there is no reason talk about Desarguesian spaces, as every projective space is Desarguesian. Also, the term Galois geometry has always been applied to geometries defined over fields (especially finite ones) whereas the Desarguesian geometries are defined over skewfields and it just happens that the finite skewfields are fields, this is not true in the infinite case, so there is some reason to keep the terms seperate. And while I'm at it, the article makes it sound like Thas and Hirschfeld invented the term ""Galois geometry"" - this implication would embarass them both. The term, as far as I know, comes from the Italian school of geometers. Most likely B. Segre is responsible, but that is only a guess.   "