Quadratic forms in models of \(I\Delta _{0}+\Omega _{1}\). I

DOI10.1016/j.apal.2007.05.004zbMath1124.03032OpenAlexW1981309831MaRDI QIDQ2382276

Paola D'Aquino, Angus J. Macintyre

Publication date: 28 September 2007

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.2007.05.004

zbMATH Keywords

quadratic formsquadratic reciprocityweak fragments of arithmetic

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Models of arithmetic and set theory (03C62) Power residues, reciprocity (11A15) Model theory (number-theoretic aspects) (11U09) General binary quadratic forms (11E16)

Related Items

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

Cites Work

• On the scheme of induction for bounded arithmetic formulas
• Combinatorial principles in elementary number theory
• Non-standard finite fields over \(I\Delta_0+\Omega_1\)
• Pell equations and exponentiation in fragments of arithmetic
• On the Computational Complexity of Determining the Solvability or Unsolvability of the Equation X 2 - DY 2 = -1
• Provability of the pigeonhole principle and the existence of infinitely many primes
• Existence and feasibility in arithmetic
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