Submission date: 11 December 2018

Abstract:

It is a problem of general interest when a domain R is first-order-definable within its field of fractions K via a universal first-order formula. We show that this is the case when K is a global field and R is finitely generated. Hereby we recover Koenigsmann's result that the ring of integers has a universal first-order definition in the field of rational numbers, as well as the generalisations of Koenigsmann's result by Park for number fields and by Eisenträger and Morrison for global function fields of odd characteristic.

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

Keywords and phrases:

Full text arXiv 1812.04372: pdf, ps.