On the number of independent orders

Abstract We investigate the model-theoretic invariant κ s r d m ( T ) , which was introduced by Shelah, and prove that κ s r d m ( T ) is sub-additive. An infinite value of κ s r d m ( T ) leads to the equality κ s r d m ( T ) = κ s r d 1 ( T ) . We apply the same proof method to analyze the other invariant κ i r d m ( T ) and show that it is also sub-additive, achieving an improvement of Shelah's result.