Mekler's Construction on NTP$_{1}$ Theories (Model theoretic aspects of the notion of independence and dimension)

Abstract

For any model M of T, one can find a graph model which is bi-interpretable with it. Extending this folklore, Mekler developed a construction method to get a group preserving many model-theoretic properties of the original one, such as stability, which Mekler himself proved. Recently, Chernikov and Hempel found another result for the case of NTP_{2} by using array lemmas on mutually indiscernible sequences. Following their results, we will show that Mekler's constrction preserves NTP_{1} by using tree lemmas on strongly indiscernible trees.