Definability of the ring of integers in some infinite algebraic extensions of the rationals

DOI10.1002/malq.201110020zbMath1281.11106OpenAlexW2010309832MaRDI QIDQ2910987

Kenji Fukuzaki

Publication date: 12 September 2012

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

Full work available at URL: https://doi.org/10.1002/malq.201110020

zbMATH Keywords

undecidabilitydefinabilityinfinite algebraic extensions

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Undecidability and degrees of sets of sentences (03D35)

Related Items

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 ⋮ 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⁾

Cites Work

• Definability of the ring of integers in pro-\(p\) Galois extensions of number fields
• The Undecidability of Algebraic Rings and Fields
• Undecidability and Definability for the Theory of Global Fields