Combinatorial principles in elementary number theory

DOI10.1016/0168-0072(91)90096-5zbMath0747.03025OpenAlexW2045616671MaRDI QIDQ1182430

Benedetto Intrigila, Alessandro Berarducci

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1016/0168-0072(91)90096-5

zbMATH Keywords

combinatorial principle\(\Delta_ 0\)- equipartition principle\(\hbox{I}\Delta_ 0\)Lagrange four squares theoremweak \(\Delta_ 0\)-pigeonhole principle

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Primes (11A41)

Related Items (14)

The prime number theorem and fragments of PA ⋮ On Grzegorczyk induction ⋮ Quadratic forms in models of \(I\Delta _{0}+\Omega _{1}\). I ⋮ Toward the limits of the Tennenbaum phenomenon ⋮ \(\text{Count}(q)\) does not imply \(\text{Count}(p)\) ⋮ End extensions of models of linearly bounded arithmetic ⋮ Integer factoring and modular square roots ⋮ Improved bounds on the weak pigeonhole principle and infinitely many primes from weaker axioms ⋮ Quadratic forms in models of \(I\Delta_0 + \Omega_1\). II: Local equivalence ⋮ A new proof of the weak pigeonhole principle ⋮ TWO (OR THREE) NOTIONS OF FINITISM ⋮ On bounded arithmetic augmented by the ability to count certain sets of primes ⋮ Non-standard finite fields over \(I\Delta_0+\Omega_1\) ⋮ Solving Pell equations locally in models of IΔ₀

Cites Work

• On the scheme of induction for bounded arithmetic formulas
• Primes and their residue rings in models of open induction
• Classes of Predictably Computable Functions
• Provability of the pigeonhole principle and the existence of infinitely many primes
• Existence and feasibility in arithmetic
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