FOLNER SEQUENCES AND HILBERT IRREDUCIBILITY THEOREM OVER Q

Let f(X; T 1, ..., T n) be an irreducible polynomial over Q. Let B be the set of b te Z n such that f(X;b) is of lesser degree or reducible over Q. Let ℱ={F j}{F j } j-1 ∞ be a Følner sequence in Z n - that is, a sequence of finite nonempty subsets F j ⊆Z n such that for each vte Z n, {Mathematical expression} Suppose ℱ satisfies the extra condition that for W a proper Q-subvariety of P n -A n and e{open}>0, there is a neighborhood U of W(R) in the real topology such that {Mathematical expression} where Z n is identified with A n (Z). We prove {Mathematical expression}. © 1990 The Weizmann Science Press of Israel.