Universally defining Z$\mathbb {Z}$ in Q$\mathbb {Q}$ with 10 quantifiers
Nicolas Daans · Journal of the London Mathematical Society · 2024
Abstract We show that for a global field , every ring of ‐integers has a universal first‐order definition in with 10 quantifiers. We also give a proof that every finite intersection of valuation rings of has an existential first‐order definition in with 3 quantifiers.