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-$$\mathsf {TP_2}$$
TP
2
iff it has 2-$$\mathsf {TP_2}$$
TP
2