Abstract
We prove that the additive structure of the ring of Laurent polynomials augmented by the predicate symbol P, where P(x) if and only if x is a power of t, is decidable. We also prove that the first-order theory of the previous structure together with the relation ∣t, where x∣ty if and only if ∃s∈Zy=x⋅ts, is undecidable.
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