2012•arXiv (Cornell University)Open access
A universal first order formula defining the ring of integers in a\n number field
Jennifer Park
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Abstract
We show that the complement of the ring of integers in a number field K is\nDiophantine. This means the set of ring of integers in K can be written as {t\nin K | for all x_1, ..., x_N in K, f(t,x_1, ..., x_N) is not 0}. We will use\nglobal class field theory and generalize the ideas originating from\nKoenigsmann's recent result giving a universal first order formula for Z in Q.\n
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