  Generalized disformal transformations enable us to construct the generalized
disformal Horndeski theories, which form the most general class of ghost-free
scalar-tensor theories to this date. We extend the effective field theory (EFT)
of cosmological perturbations to incorporate these generalized disformal
Horndeski theories. The main difference from the conventional EFT is that our
extended EFT involves operators with higher spatial derivatives of the lapse
function. Our EFT also accommodates the generalized disformal transformation of
U-DHOST theories.
