Arithmetical complexity of the language of generic limit sets of cellular automata

The generic limit set of a dynamical system is the smallest that attracts most space in topological sense: it closed with comeager basin attraction. Introduced by Milnor, has been studied context one-dimensional cellular automata Djenaoui and Guillon, Delacourt, Törmä. In this article we present complexity bounds on realizations sets prescribed properties. We show have Π20 language if they are inclusion-minimal, Σ10 automaton equicontinuous points, these tight. also prove many chain mixing subshifts all Δ20 realizable as sets. As corollary, characterize minimal occur