Finite canonization

The canonization theorem says that for given m,n for some m^* (the first one is called ER(n;m)) we have: for every function f with domain [{1, ...,m^*}]^n, for some A in [{1, ...,m^*}]^m, the question of when the equality f({i_1, ...,i_n})=f({j_1, ...,j_n}) (where i_1< ...