Definitions, preliminary results

Consider the language C = { + , - , * , 0 , 1, <r}, where + , - , • are binary op­ erations, 0,1 are constants, and a is a unary function symbol. Then every difference field is naturally an /^-structure. Inclusion of difference fields corre­ sponds to inclusion of ^ -structures, and similarly for morphisms of difference fields. A good reference for basic results on difference fields is R. M. Cohn’s Difference algebra [1].