Abstract
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.
Citation
Alexandra Shlapentokh. "Existential definability with bounds on archimedean valuations." J. Symbolic Logic 68 (3) 860 - 878, September 2003. https://doi.org/10.2178/jsl/1058448445
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