THE DIOPHANTINE PROBLEM FOR ADDITION AND DIVISIBILITY OVER SUBRINGS OF THE RATIONALS

DOI10.1017/jsl.2016.64zbMath1431.11138OpenAlexW2750677713MaRDI QIDQ5359580

Carlos Azarel Martínez-Ranero, Leonidas Cerda-Romero

Publication date: 26 September 2017

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/jsl.2016.64

zbMATH Keywords

small ringspositive-existential definability\(S\)-integers

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Interpolation, preservation, definability (03C40)

Related Items (2)

Existential decidability for addition and divisibility in holomorphy subrings of global fields ⋮ The diophantine problem for addition and divisibility for subrings of rational functions over finite fields

Cites Work

• Unnamed Item
• Decidability of the universal theory of natural numbers with addition and divisibility
• Defining Integers
• On the 𝑟-rank Artin Conjecture
• Decidability of Sub-theories of Polynomials over a Finite Field
• An Undecidability Result for Power Series Rings of Positive Characteristic. II
• Undecidable Existential Problems for Addition and Divisibility in Algebraic Number Rings. II
• The Diophantine Problem for Addition and Divisibility
• Undecidable Existential Problems for Addition and Divisibility in Algebraic Number Rings
• Hilbert's Tenth Problem is Unsolvable
• Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of $\mathbb {Q}$
• Model Theory
• Definability and decision problems in arithmetic

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