Existential definability with Bounds on archimedean valuations

Journal of Symbolic Logic 68 (3):860-878 (2003)
We show that a solution to Hilbert's Tenth Problem in the rings of algebraic integers and bigger subrings of number fields where it is currently not known, is equivalent to a problem of bounding archimedean valuations over non-real number fields
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DOI 10.2178/jsl/1058448445
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