Defining \(\mathbb{Z}\) using unit groups
From MaRDI portal
Publication:6595585
DOI10.4064/AA230505-6-6MaRDI QIDQ6595585
Barry Mazur, Karl Rubin, Alexandra Shlapentokh
Publication date: 30 August 2024
Published in: Acta Arithmetica (Search for Journal in Brave)
Decidability (number-theoretic aspects) (11U05) Decidability of theories and sets of sentences (03B25)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I.
- Diophantine definability and decidability in large subrings of totally real number fields and their totally complex extensions of degree 2
- Towards Hilbert's tenth problem for rings of integers through Iwasawa theory and Heegner points
- Division-ample sets and the Diophantine problem for rings of integers
- Ranks of twists of elliptic curves and Hilbert's tenth problem
- Rings of algebraic numbers in infinite extensions of \(\mathbb Q\) and elliptic curves retaining their rank
- Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of \(\mathbb{Q}\)
- Definability of the ring of integers in pro-\(p\) Galois extensions of number fields
- First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers
- Diophantine definability and decidability in extensions of degree 2 of totally real fields
- Elliptic curves, \(L\)-functions, and Hilbert's tenth problem
- A note on the Northcott property and undecidability
- Unit Equations in Diophantine Number Theory
- Definability of the natural numbers in totally real towers of nested square roots
- Extension of Hilbert's tenth problem to some algebraic number fields
- Hilbert's Tenth Problem for a Class of Rings of Algebraic Integers
- Diophantine relationships between algebraic number fields
- Elliptic curves retaining their rank in finite extensions and Hilbert's Tenth Problem for rings of algebraic numbers
- Arithmetic over the rings of all algebraic integers.
- Elimination theory for the ring of algebraic integers.
- Diophantine Sets Over Algebraic Integer Rings. II
- Hilbert's Tenth Problem for Quadratic Rings
- Diophantine Sets over Some Rings of Algebraic Integers
- On the constructible numbers
- Hilbert's Tenth Problem is Unsolvable
- The undecidability of cyclotomic towers
- On Diophantine definability and decidability in some infinite totally real extensions of ℚ
- On the Northcott property and local degrees
- Julia Robinson numbers and arithmetical dynamic of quadratic polynomials
- Undecidability, unit groups, and some totally imaginary infinite extensions of ℚ
- Undecidability of ℚ⁽²⁾
- Julia Robinson numbers
- Undecidability in Number Theory
- Unsolvable Diophantine Problems
- An Unsolvable Problem of Elementary Number Theory
- Definability and decision problems in arithmetic
- Big fields that are not large
- Extensions of some theorems of Gödel and Church.
- Superficies elípticas y el décimo problema de Hilbert
- Definability and decidability for rings of integers in totally imaginary fields
- Corrigendum to: ``Existential definability and Diophantine stability
Related Items (1)
This page was built for publication: Defining \(\mathbb{Z}\) using unit groups
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6595585)