3
Quantifier Rank
• qr(f) is defined as before:
•In general it can be an ordinal, e.g. 5, 99, w+3, 4w + 7, etc
•Over finite structures, we will show that it suffices to have qr · w
qr(Çi 2 I fi) = qr(Æi 2 I fi) = supi2 I qr(fi)
qr(9 x.f) = qr(8 x.f) = qr(f) + 1