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20042024
most citedDiophantine definability of infinite discrete non-archimedean sets and Diophantine models over large subrings of number fields

12 citations · 33 across the 23 of their papers we have counts for

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Showing 2013 · math.NTShow all

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math.NT2013

First Order Decidability and Definability of Integers in Infinite Algebraic Extensions of Rational Numbers

Alexandra Shlapentokh

We extend results of Videla and Fukuzaki to define algebraic integers in large classes of infinite algebraic extensions of Q and use these definitions for some of the fields to sho…

math.NT2013★ 3 cited

Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field

Kirsten Eisentraeger, Alexandra Shlapentokh

We prove that the existential theory of any function field of characteristic is undecidable in the language of rings provided that the constant field does not contain th…