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Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of Q
Annals of Pure and Applied Logic 68 (3):299-325 (1994)
Abstract
This paper provides the first examples of rings of algebraic numbers containing the rings of algebraic integers of the infinite algebraic extensions of where Hilbert's Tenth Problem is undecidableAuthor's Profile
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Citations of this work
On Diophantine definability and decidability in some rings of algebraic functions of characteristic 0.Alexandra Shlapentokh - 2002 - Journal of Symbolic Logic 67 (2):759-786.
Diophantine definability over non-finitely generated non-degenerate modules of algebraic extensions of ℚ.Alexandra Shlapentokh - 2001 - Archive for Mathematical Logic 40 (4):297-328.
Rings of algebraic numbers in infinite extensions of $${\mathbb {Q}}$$ and elliptic curves retaining their rank.Alexandra Shlapentokh - 2009 - Archive for Mathematical Logic 48 (1):77-114.
References found in this work
A Diophantine definition of rational integers over some rings of algebraic numbers.Alexandra Shlapentokh - 1992 - Notre Dame Journal of Formal Logic 33 (3):299-321.
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