Intersections of sequences of ideals generated by polynomials

We present a method for determining the reduced Grobner basis with respect to a given admissible term order of order type omega, of the intersection ideal of an infinite sequence of polynomial ideals. As an application we discuss the Lagrange type interpolation on algebraic sets and the "approximation" of the ideal I of an algebraic set by zero dimensional ideals, whose affine Hilbert functions converge towards the affine Hilbert function of I. (C) 1998 Elsevier Science B.V. All rights reserved.