25
0/1 Law for FO
•
Lemma
For every extension axiom
t
,
m
(
t
) = lim
n
m
n
(
t
) = 1
•
Proof
: later
•
•
Corollary
For any m extension axioms
t
1
, …,
t
m
:
m
(
t
1
Æ
…
Æ
t
m
) = 1
•
Proof
m
n
(
:
(
t
1
Æ
…
Æ
t
m
))
=
m
n
(
:
t
1
Ç
…
Ç
:
t
m
)
·
m
n
(
:
t
1
) + … +
m
n
(
:
t
m
)
!
0