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Preprint Number 430

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430. Jennifer Park
A universal first order formula defining the ring of integers in a number field

Submission date: 1 March 2012.


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.

Mathematics Subject Classification: 11R37 (Primary) 11R52, 11U05 (Secondary)

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Full text arXiv 1202.6371: pdf, ps.

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