Model Theory and Combinatorics of Banned Sequences

Abstract

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 $ \operatorname {\mathrm{op}}$ -rank, a notion of Guingona and Hill [4].

Tree Dimension and the Sauer-Shelah Dichotomy

“…solutions. 3 Bhaskar calls this quantity "thicket dimension" in [2, Definition 3.6] but notes its other names in a remark. See also [1,Definition 8] and [4].…”