15
Fagin’s Theorem
•
Theorem
[Fagin]
9
SO captures precisely NP
•
•
More precisely:
•
For every
f
2
9
SO, the problem of
checking whether A
˛
f
is in NP
•
For any property of models, P, s.t. checking
A
2
P is in NP, there exists a formula
f
2
9
SO s.t. A
˛
f
iff A
2
P