MODEL THEORY AND COMBINATORICS OF BANNED SEQUENCES

We set up a general context in which one can prove Sauer-Shelah type lemmas. We apply our general results to answer a question of Bhaskar [1] and give a slight improvement to a result of Malliaris and Terry [7]. We also prove a new Sauer-Shelah type lemma in the context of op-rank, a notion of Guingona and Hill [4].

Automated summary

We establish a general context for proving Sauer-Shelah type lemmas and apply it to answer a question and improve an existing result. We also prove a new Sauer-Shelah type lemma in the context of op-rank.