Rings of algebraic numbers in infinite extensions of \(\mathbb Q\) and elliptic curves retaining their rank

DOI10.1007/s00153-008-0118-yzbMath1179.11048arXiv0705.4324OpenAlexW2085881424MaRDI QIDQ1005933

Alexandra Shlapentokh

Publication date: 17 March 2009

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.4324

zbMATH Keywords

elliptic curveHilbert's tenth problemDiophantine definition

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Elliptic curves over global fields (11G05)

Related Items (8)

ELLIPTIC CURVE POINTS AND DIOPHANTINE MODELS OF ℤ IN LARGE SUBRINGS OF NUMBER FIELDS ⋮ First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers ⋮ Definability of the natural numbers in totally real towers of nested square roots ⋮ Existential definability and diophantine stability ⋮ Definability and decidability for rings of integers in totally imaginary fields ⋮ Extensions of Hilbert’s Tenth Problem: Definability and Decidability in Number Theory ⋮ Defining Integers ⋮ Big fields that are not large

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