•The k-back-and-forth equivalence relation 'k is defined as follows:
•
•A '0 B
iff the substructures induced by the constants in A and B are isomorphic
•A 'k+1 B
iff the following hold:
–Forth: 8 a 2 A 9 b 2 B s.t. (A,a) 'k (B,b)
–Back: 8 b 2 B 9 a 2 A s.t. (A,a) 'k (B,b)