Remarks on undecidability of indecomposable polynomial rings

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 for all members in this class of rings.

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Bibliographic Details
Published in:arXiv.org 2023-09
Main Authors: Barone, Marco, Caro-Montoya, Nicolás, Naziazeno, Eudes
Format: Article
Language:English
Subjects:
Arithmetic
Mathematical analysis
Polynomials
Rings (mathematics)
Online Access:Get full text
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Description
Summary: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 for all members in this class of rings.
ISSN:2331-8422