[FOM] geometry and mathematical logic

Rupert McCallum rupertmccallum at yahoo.com
Wed Aug 5 00:54:23 EDT 2009

The fundamental theorem of projective geometry states that a bijection from a projective space of dimension greater than one to itself which sends straight lines onto straight lines is a projective transformation possibly composed with an automorphism of the underlying field. This result can be viewed as a consequence of the fact that projective geometry can be interpreted in the theory of fields and vice versa.

Tits showed that the fundamental theorem of projective geometry generalises to a result about the automorphism group of the building of a split semisimple algebraic group G defined over a field k of rank greater than one. The result stated above is a consequence of the special case where G=SL(n,k), n>2. The other cases give information about various other geometries.

Has any work been done relating this more general result to results in mathematical logic?

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