•FO[k] = all formulas of
quantifier rank · k
•
•Definition Let A be a structure and a be an
m-tuple in A. The rank-k m-type
of a over A is
tpk(A,a) = {f 2 FO[k] with m free
vars | A ² f(a) }
•
•How any distinct rank-k
types are there ? [finitely or infinitely
many ?]