2 papers
math.LO2023
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…
math.LO2017
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…