4 papers
Remarks on undecidability of indecomposable polynomial rings
Marco Barone, Nicolás Caro-Montoya, Eudes Naziazeno
We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability…
Interpretability and uniform definability of integers, and undecidability of reduced indecomposable polynomial rings
Marco Barone, Nicolás Caro, Eudes Naziazeno
We prove first-order definability of the prime subring inside polynomial rings, whose coefficient rings are (commutative unital) reduced and indecomposable. This is achieved by mea…
The logical complexity of finitely generated commutative rings
Matthias Aschenbrenner, Anatole Khélif, Eudes Naziazeno +1
We characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring is bi-interpretabl…
On the definability of rational integers in a class of rings
Eudes Naziazeno
We provide a sufficient condition for a polynomial ring, not necessarily commutative, to have a first-order definition for the rational integers.