  The Horndeski action is the most general one involving a metric and a scalar
field that leads to second-order field equations in four dimensions. Being the
natural extension of the well-known scalar-tensor theories, its structure and
properties are worth analyzing along the experience accumulated in the latter
context. Here, we argue that disformal transformations play, for the Horndeski
theory, a similar role to that of conformal transformations for scalar-tensor
theories a la Brans-Dicke.
