Universally and existentially definable subsets of global fields

Kirsten Eisenträger, Travis Morrison

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We show that rings of S-integers of a global function field K of odd characteristic are first-order universally definable in K. This extends work of Koenigsmann and Park who showed the same for ℤ in ℚ and the ring of integers in a number field, respectively. We also give another proof of a theorem of Poonen and show that the set of non-squares in a global field of characteristic ≠ 2 is diophantine. Finally, we show that the set of pairs (x, y) ∈ K˟ x K˟ such that x is not a norm in K(√y) is diophantine over K for any global field K of characteristic ≠ 2.

Original languageEnglish (US)
Pages (from-to)1173-1204
Number of pages32
JournalMathematical Research Letters
Issue number4
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics


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