Simulation of effective subshifts by two-dimensional subshifts of finite type

In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction.). There exists a correspondence between the notion of simulation and the set of forbidden patterns. The main result of this paper states that any effective subshift of dimension d - that is a subshift whose set of forbidden patterns can be generated by a Turing machine - can be obtained by applying dynamical operations on a subshift of finite type of dimension d+1 - a subshift that can be defined by a finite set of forbidden patterns. This result improves Hochman's (Invent. Math. 176(1):131-167, 2009).