An extension of the Cobham-Semenov theorem

摘要

Let θ, θ' be two multiplicatively independent Pisot numbers, and let U, U' be two linear numeration systems whose characteristic polynomial is the minimal polynomial of θ and θ', respectively. For every n ≥ 1, if A is contained in N~n is U- and U'-recognizable then A is definable in (N; +).