Quantifier Elimination
Like the theory of algebraically closed fields, the theory DCF0 of differentially closed fields of characteristic 0 eliminates quantifiers. The geometric content of this statement is that the projection of a d-constructible set is d-constructible. It also eliminates imaginaries, is complete, and model complete.
In characteristic p>0, the theory DCFp eliminates quantifiers in the language of differential fields with a unary function r added that is the pth root of all constants, and is 0 on elements that are not constant.
Read more about this topic: Differentially Closed Field
Famous quotes containing the word elimination:
“The kind of Unitarian
Who having by elimination got
From many gods to Three, and Three to One,
Thinks why not taper off to none at all.”
—Robert Frost (1874–1963)