A universal first order formula defining the ring of integers in a number field
Number Theory
2012-03-01 v1
Abstract
We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_N in K, f(t,x_1, ..., x_N) is not 0}. We will use global class field theory and generalize the ideas originating from Koenigsmann's recent result giving a universal first order formula for Z in Q.
Keywords
Cite
@article{arxiv.1202.6371,
title = {A universal first order formula defining the ring of integers in a number field},
author = {Jennifer Park},
journal= {arXiv preprint arXiv:1202.6371},
year = {2012}
}
Comments
19 pages