3
Quantifier Rank
•
qr(
f
) is defined as before:
•
•
•
•
•
In general it can be an ordinal, e.g. 5, 99,
w
+3, 4
w
+ 7, etc
•
Over
finite
structures, we will show that it suffices
to have qr
·
w
qr(
Ç
i
2
I
f
i
) = qr(
Æ
i
2
I
f
i
) = sup
i
2
I
qr(
f
i
)
qr(
9
x.
f
) = qr(
8
x.
f
) = qr(
f
) + 1