We study the theory of the structure induced by parameter free formulas on a “dense” algebraically independent subset of a model of a geometric theory T . We show that while being a trivial geometric theory, inherits most of the model theoretic complexity of T related to stability, simplicity, rosiness, the NIP and the NTP 2 . In particular, we show that T is strongly minimal, supersimple of SU‐rank 1, has the NIP or the NTP 2 exactly when has these properties. We show that if T is superrosy of thorn rank 1, then so is , and that the converse holds if T satisfies acl = dcl.