Abstract :
For a pseudovariety image of ordered semigroups, let image be the class of sofic subshifts whose syntactic semigroup lies in image. It is proved that if image contains image then image is closed under taking shift equivalent subshifts, and conversely, if image is closed under taking conjugate subshifts then image contains image and image. Almost finite type subshifts are characterized as the irreducible elements of image, which gives a new proof that the class of almost finite type subshifts is closed under taking shift equivalent subshifts.
