Definability and decidability in infinite algebraic extensions

DOI10.1016/j.apal.2014.02.001zbMath1352.12006arXiv1105.2792OpenAlexW2057338786MaRDI QIDQ2349099

Carlos R. Videla, Alexandra Shlapentokh

Publication date: 17 June 2015

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.2792

zbMATH Keywords

first-order definabilityinfinite algebraic extensions

Mathematics Subject Classification ID

Decidability and field theory (12L05) Model-theoretic algebra (03C60) Model theory of fields (12L12) Other model constructions (03C30)

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Cites Work

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• Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic fields
• Einige unentscheidbare Körpertheorien
• Definability of the ring of integers in pro-\(p\) Galois extensions of number fields
• The Undecidability of Algebraic Rings and Fields
• Characterizing integers among rational numbers with a universal-existential formula
• Arithmetic over the rings of all algebraic integers.
• Elimination theory for the ring of algebraic integers.
• Undecidability and Definability for the Theory of Global Fields
• On the constructible numbers
• Rumely’s local global principle for algebraic 𝑃𝒮𝒞 fields over rings
• The undecidability of cyclotomic towers
• Hilbert’s Tenth Problem: Relations with Arithmetic and Algebraic Geometry
• Model Theory
• Elliptic curves and Hilbert’s tenth problem for algebraic function fields over real andp-adic fields
• Definability and decision problems in arithmetic
• Undecidable Rings

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