A universal first order formula defining the ring of integers in a number field

Details A universal first order formula defining the ring of integers in a number field A universal first order formula defining the ring of integers in a number field

2012-02-28

arxiv.org/abs/1202.6371v1

Mathematics

Number Theory

19 pages

Scientific paper

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.

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