The authors show, by means of a finitary version
□finλ, D of the combinatorial principle
□b*λ of [7], the consistency of the
failure, relative to the consistency of supercompact cardinals, of
the following: for all regular filters D on a cardinal
λ, if Mi and Ni are elementarily equivalent models
of a language of size ≤ λ, then the second player has a
winning strategy in the Ehrenfeucht-Fraïssé game of length
λ+ on ∏i Mi/D and ∏i Ni/D. If in
addition 2λ=λ+ and i <λ implies
|Mi|+|Ni|≤ λ+ this means that the ultrapowers are
isomorphic. This settles negatively conjecture 18 in [2].