4
Example
•
Over ordered finite structures, every
property can be expressed in L
m+1
1
,
w
, where
m = max
i
(arity(R
i
)),
R
i
2
s
•
•
Proof:
•
First, show that if
s
= {<} then every
property on finite linear orders is in L
m+1
1
,
w
•
Next, generalize to arbitrary
s