
112
Apt, Blair,
and
Walker
THEOREM 8
Μ ρ is a minimal model of P. •
Note that in view of Lemmas 6 and 2 and Theorems 4 and 6, M
p
is a model
of Ρ whenever the sequence P
v
...,P
n
defines new relations. But to prove that
Μ ρ is supported we also need Lemma 7, which requires that all T
p
are grow-
ing. This condition is satisfied (see Theorem 5) if each P. is semi-positive.
Now it is easy to see that if the sequence P
v
...,P
n
defines new relations and
each P. is semi-positive, then Ρ is stratified by Ρ = P
x
Ù ... ÙP
n
. In other
words, our general results on nonmonotonic operators do not allow us to con-
clude existence of supported models for other tha ...