The local dynamical structure of Δ* sets via a new Furstenberg family algebra
This development formalizes in Lean 4 the results of the paper "The local dynamical structure of Δ* sets via a new Furstenberg family algebra", which strengthens the connection between the combinatorics of difference sets and the dynamics of group rotations. Let S be a discrete semigroup. A set A ⊆ S is syndetic if there is a finite F ⊆ S with S = ∪_{f ∈ F} f⁻¹A; a Δ set if there is a sequence s₁, s₂, … in S with s_j ∈ s_i A for all i < j; and a Bohr_0 set if it contains the preimage of an open neighborhood of the identity under a semigroup homomorphism from S to a finite-dimensional torus.…
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