The Model Theory of Algebraically Closed Fields
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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.
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Daniel Cook (2000). The Model Theory of Algebraically Closed Fields. UWSpace. http://hdl.handle.net/10012/1066