22
Gaifman’s Theorem
•
Theorem [Gaifman] Let
s
be relational.
Then every FO sentence over
s
is
equivalent to a Boolean combination of
sentences of the form:
9
x
1
…
9
x
s
(
Æ
i=1,s
a
(r)
(x
i
))
Æ
(
Æ
1
·
i < j
·
s
d
>2r
(x
i
, x
j
))