Quadratic forms in models of \(I\Delta_0 + \Omega_1\). II: Local equivalence

DOI10.1016/j.apal.2010.12.003zbMath1230.03090OpenAlexW2081072735MaRDI QIDQ639651

Paola D'Aquino, Angus J. Macintyre

Publication date: 22 September 2011

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2010.12.003

zbMATH Keywords

quadratic formscompletionsweak fragments of arithmetic

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Nonstandard models of arithmetic (03H15) Quadratic forms over local rings and fields (11E08)

Cites Work

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• Relative elimination of quantifiers for Henselian valued fields
• Combinatorial principles in elementary number theory
• Non-standard finite fields over \(I\Delta_0+\Omega_1\)
• Pell equations and exponentiation in fragments of arithmetic
• Quadratic forms in models of \(I\Delta _{0}+\Omega _{1}\). I
• Diophantine problems over local fields. III: Decidable fields
• Local behaviour of the Chebyshev theorem in models of I⊿₀
• Provability of the pigeonhole principle and the existence of infinitely many primes
• Solving Pell equations locally in models of IΔ₀
• From p-rigid elements to valuations (with a Galois-characterization of p-adic fields).
• Diophantine Problems Over Local Fields I
• Existence and feasibility in arithmetic

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