Defining \(\mathbb Z\) in \(\mathbb Q\)

DOI10.4007/annals.2016.183.1.2zbMath1390.03032arXiv1011.3424OpenAlexW2964004208MaRDI QIDQ5962625

Jochen Koenigsmann

Publication date: 15 February 2016

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.3424

zbMATH Keywords

undecidabilityHilbert's 10th problemdefinablityDiophantine equation

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Undecidability and degrees of sets of sentences (03D35) Interpolation, preservation, definability (03C40) Model theory (number-theoretic aspects) (11U09) Diophantine equations (11Dxx)

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Cites Work

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• Mathematical logic and model theory. A brief introduction
• The set of nonsquares in a number field is diophantine
• A universal first-order formula defining the ring of integers in a number field
• Characterizing integers among rational numbers with a universal-existential formula
• From p-rigid elements to valuations (with a Galois-characterization of p-adic fields).
• Elliptic divisibility sequences and undecidable problems about rational points

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