9
Proof of the Lemma
1.Claim:
there are only finitely many inequivalent FOk formulas over R
[Proof: in class ?? ]
a1, a2, …, am
Hence:
R ² 8 x(p(x) $ ai(x))
R ² 8 x(: ai $ : aj)
R ² 8 x.(9 xj.ai $ al)
Let yk be their conjunction; clearly R ² fk
[Proof: in class ?? ]
a1, a2, …, am
Hence:
R ² 8 x(p(x) $ ai(x))
R ² 8 x(: ai $ : aj)
R ² 8 x.(9 xj.ai $ al)
Let yk be their conjunction; clearly R ² fk
Closure axioms