Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4662022 | Annals of Pure and Applied Logic | 2012 | 5 Pages |
Abstract
We prove that the additive structure of the ring of Laurent polynomials augmented by the predicate symbol PP, where P(x)P(x) if and only if xx is a power of tt, is decidable. We also prove that the first-order theory of the previous structure together with the relation ∣t∣t, where x∣tyx∣ty if and only if ∃s∈Zy=x⋅ts, is undecidable.
► We study the additive structure of the ring of Laurent polynomials, say AA. ► We show decidability of first-order theory of AA augmented by relation for powers of tt. ► We study the previous structure together with a weak form of divisibility, say BB. ► We prove that the first-order theory of BB is undecidable.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Alla Sirokofskich,