# Cohomology Theories on The Stone Space of Complete n-types

Just a random thought here: Can cohomology theories (e.g. sheaf cohomology) on the Stone space $S_n(T)$ (the space of complete n-types) of a first-order theory $T$ tell us anything interesting (e.g. the classification of theories)? Is there any result in model theory that is obtained (probably most easily) by this kind of application of cohomology theories? Thanks!

• I am not aware of any such result. But don't cohomology theories have problems with zero dimensional spaces? The spaces of types are zero-dimensional. I don't know about sheaf cohomology, though. Jul 22 '10 at 8:55
• @Stefan: indeed, you were right. The (sheaf-)cohomological dimension of the type spaces is always zero. So sheaf cohomology can't really give anything more interesting than the global section functor. Apr 7 '11 at 15:17
• Maybe you should put it as an answer so that I can accept it? Apr 7 '11 at 15:22