First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers

DOI10.1007/s11856-018-1708-yzbMath1436.03204arXiv1307.0743OpenAlexW2964318116WikidataQ129711961 ScholiaQ129711961MaRDI QIDQ1659540

Alexandra Shlapentokh

Publication date: 22 August 2018

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.0743

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Model-theoretic algebra (03C60) Decidability of theories and sets of sentences (03B25) Interpolation, preservation, definability (03C40)

Related Items (9)

Definability of the natural numbers in totally real towers of nested square roots ⋮ Existential definability and diophantine stability ⋮ Northcott numbers for the house and the Weil height ⋮ Definability and decidability for rings of integers in totally imaginary fields ⋮ A TOPOLOGICAL APPROACH TO UNDEFINABILITY IN ALGEBRAIC EXTENSIONS OF ⋮ Undecidability, unit groups, and some totally imaginary infinite extensions of ℚ ⋮ Extensions of Hilbert’s Tenth Problem: Definability and Decidability in Number Theory ⋮ Undecidability of ℚ⁽²⁾ ⋮ On the Northcott property and local degrees

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