Canonical Equivalence Relations on ℚn

We show that for each positive integer n there is a finite list of equivalence relations on [ℚ]n with the property that for every other equivalence relation E on [ℚ]n there is X⊂ℚ of order type equal to the order type of ℚ, such that E↾[X]n is equal to one of the equivalence relations from the list.