5
Proof
•
Let
a
1
(
x
), …,
a
s
(
x
) be all quantifier free
types with k variables (i.e. in FO
k
[0])
•
•
y
0
(
x
,
y
) =
Ç
i
¹
j
(
a
i
(
x
)
Æ
a
j
(
y
))
•
•
y
(R,
x
,
y
) =
y
0
(
x
,
y
)
Ç
((
Ç
i=1,k
9
x
i
8
y
i
R(
x
,
y
))
Æ
(
Ç
i=1,k
9
y
i
8
x
i
R(
x
,
y
))