This is a file in the archives of the Stanford Encyclopedia of Philosophy. |
Proof.
We have shown that K*N(E) is a fixed point of fE, so we only need to show that K*N(E) is the greatest fixed point. Let B be a fixed point of fB. We want to show that B KkN(E) for each value k1. We will proceed by induction on k. By hypothesis,
We alo have:
(i) K1N(B) K1NK mN(E) = Km+1N(E)
by monotonicity, so combining (i) and (ii) we have:
(ii) B = K1N(EB) K1N(B)
B K1N(B) Km+1N(E)completing the induction.
First published: June 12, 2002
Content last modified: June 12, 2002