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:
“To reduce the imagination to a state of slaveryeven though it would mean the elimination of what is commonly called happinessis to betray all sense of absolute justice within oneself. Imagination alone offers me some intimation of what can be.”
—André Breton (18961966)