26 October 2004 4:00 - 5:30 Jim Loveys Linear reducts of the complex field Abstract: A {\em reduct} of a first-order structure is simply a structure with the same underlying set, but possibly fewer definable sets. (We allow parameters in the definitions.) If we start with the structure that is the field of complex numbers, it has many reducts, a great number of which are trivial in a certain sense. Any such reduct has a kind of combinatorial geometry (akin to that provided by linear span in vector spaces). If the closed sets yield a distributive lattice, we consider the reduct trivial. If it is not trival in this sense, but the reduct is proper (not the entire field), we call it {\em linear}. We give a list of linear reducts, which is complete up to a finite cover. (That is, for any linear reduct M, there is a constructible map f with finite fibres such that f(M) with the induced structure is on our list.)