The Model Theory of Algebraically Closed Fields
Model theory can express properties of algebraic subsets of complex n-space. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of formulas, called types. Moreover, the topological dimension of a constructible set is equal to the Morley rank of the formula which defines it.
Cite this version of the work
Daniel Cook (2000). The Model Theory of Algebraically Closed Fields. UWSpace. http://hdl.handle.net/10012/1066