An extension of the Cobham-Semënov Theorem

Journal of Symbolic Logic 65 (1):201-211 (2000)
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Abstract

Let θ, θ′ be two multiplicatively independent Pisot numbers, and letU,U′ be two linear numeration systems whose characteristic polynomial is the minimal polynomial of θ and θ′, respectively. For everyn≥ 1, ifA⊆ ℕnisU-andU′ -recognizable thenAis definable in 〈ℕ: + 〉.

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10.2307/2586532

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Weak Second‐Order Arithmetic and Finite Automata.J. Richard Büchi - 1960 - Mathematical Logic Quarterly 6 (1-6):66-92.

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