Positive indiscernibles

We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str \(_0\) ${}_0$ -trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing—rather than locally basing or EM-basing—str-trees on s-trees and str \(_0\) ${}_0$ -trees on str-trees. As an application we show that a thick positive theory has k- \(\mathsf {TP_2}\) ${\mathsf{TP}}_{\mathsf{2}}$ iff it has 2- \(\mathsf {TP_2}\) ${\mathsf{TP}}_{\mathsf{2}}$