Universally defining Z$\mathbb {Z}$ in Q$\mathbb {Q}$ with 10 quantifiers
Nicolas Daans
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.
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