4
Example
•
Recall: EVEN(
A
) is not expressible in FO
•
Let
s
<,+
= {<,+}
•
Consider
A
2
STRUCT[
s
<,+
] s.t.
–
< is interpreted as a linear order a
1
< … < a
n
–
(a
i
, a
j
, a
k
)
2
+
iff
i+j=k
•
Then, we can write a sentence
f
that checks
EVEN(
A
)
[
HOW ?? ]