9
The Proof
•
Idea: recall that we can express EVEN in MSO(<).
Let S(x,y) =
:
(
9
z.x<z
Æ
z<y)
Æ
x < y
•
•
•
•
•
We can’t say
9
P in FO.
Instead, we will use a
vocabulary
s
that allows to assert the existence of
all
2
n
sets P.
9
P.(
8
x.y.(S(x,y)
)
(P(x)
Æ:
P(y)
Ç
:
P(x)
Æ
P(y))
Æ
P(min)
Æ
:
P(max))
EVEN=