KEISLER'S ORDER IS NOT LINEAR, ASSUMING A SUPERCOMPACT

We show that if there is a supercompact cardinal, then Keisler's order is not linear. More specifically, let T-n,T-k be the theory of the generic n-clique free k-ary graph for any n > k >= 3, and let T-Cas be the simple nonlow theory described by Casanovas in [2]. Then we show that T-Cas (sic) T-n,T-k always, and if there is a supercompact cardinal then T-n,T-k (sic) T-Cas.