Submission date: 5 January 2023

Abstract:

We show that for a global field K, every ring of S-integers has a universal first-order definition in K with 10 quantifiers. We also give a proof that every finite intersection of valuation rings of K has an existential first-order definition in K with 3 quantifiers.

Mathematics Subject Classification: 11U99 (Primary) 11U05, 11R52 (Secondary)

Keywords and phrases:

Full text arXiv 2301.02107: pdf, ps.