21
Gaifman’s Theorem
•
Definition
A formula
f
(x) is r-local if all its
quantifiers are bounded to B
r
(x):
–
9
z.
y
è
9
z. (z
2
B
r
(x))
Æ
y
–
8
z.
y
è
8
z.(z
2
B
r
(x))
)
y
)
–
•
We write
f
(r)
to emphasize that
f
is r-local.