Universally defining Z$\mathbb {Z}$ in Q$\mathbb {Q}$ with 10 quantifiers

DOI10.1112/jlms.12864arXiv2301.02107OpenAlexW4391387382MaRDI QIDQ6200274

Nicolas Daans

Publication date: 29 February 2024

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.02107

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Connections of number theory and logic (11U99)

Cites Work

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• Further results on Hilbert's tenth problem
• Diophantine classes of holomorphy rings of global fields
• Universally and existentially definable subsets of global fields
• Universally defining finitely generated subrings of global fields
• A universal first-order formula defining the ring of integers in a number field
• Characterizing integers among rational numbers with a universal-existential formula
• Irreducibility of polynomials over global fields is diophantine
• Definability and decision problems in arithmetic
• Defining \(\mathbb Z\) in \(\mathbb Q\)
• $\mathbb Q\setminus \mathbb Z$ is diophantine over $\mathbb Q$ with $32$ unknowns

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