Geodesic
Decidability of the class of all the rings $\mathbb {Z}/m\mathbb {Z}$: A problem of Ax
Forum of Mathematics, Sigma, Tome 11 (2023)

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We prove that the class of all the rings $\mathbb {Z}/m\mathbb {Z}$ for all $m>1$ is decidable. This gives a positive solution to a problem of Ax asked in his celebrated 1968 paper on the elementary theory of finite fields [1, Problem 5, p. 270]. In our proof, we reduce the problem to the decidability of the ring of adeles $\mathbb {A}_{\mathbb {Q}}$ of $\mathbb {Q}$. 
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Jamshid Derakhshan; Angus Macintyre. Decidability of the class of all the rings $\mathbb {Z}/m\mathbb {Z}$: A problem of Ax. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.62

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