Abstract:
For each 
there exist a model 
of
which satisfies the Count(p) principle. Furthermore
if p contain all prime factors of q there exist 
and a bijective map 
mapping 
onto 
.
A corollary is a complete classification of the Count(q) versus Count(p) problem. Another corollary solves an open question by M. Ajtai.
Available as PostScript, PDF, DVI.