A CHARACTERIZATION OF ω-LIMIT SETS IN SUBSHIFTS OF BAIRE SPACE

The paper proves that for a subshift of finite type over a countably infinite alphabet, a subset Z is an ω-limit set iff it is closed and invariant (Theorem 23), via a construction that interleaves an enumeration of initial segments from Z with “marker” symbols not appearing in the finite forbidden basis; this yields x with ω(x)=Z . The candidate solution gives the same marker-based construction (with slightly stronger ‘disjoint marker-blocks’), checks x∈Γ, proves Z⊆ω(x) and ω(x)⊆Z, and explicitly treats Z=∅. Apart from that minor explicit empty-set addendum (not spelled out in the paper’s sketch), the arguments are essentially the same.