Combinatorial Principles in Elementary Number Theory

@article{Berarducci1991CombinatorialPI,
  title={Combinatorial Principles in Elementary Number Theory},
  author={A. Berarducci and B. Intrigila},
  journal={Ann. Pure Appl. Log.},
  year={1991},
  volume={55},
  pages={35-50}
}
Abstract We prove that the theory IΔ 0 , extended by a weak version of the Δ 0 -Pigeonhole Principle, proves that every integer is the sum of four squares (Lagrange's theorem). Since the required weak version is derivable from the theory IΔ 0 + ∀ x ( x log( x ) exists), our results give a positive answer to a question of Macintyre (1986). In the rest of the paper we consider the number-theoretical consequences of a new combinatorial principle, the ‘Δ 0 -Equipartition Principle’ (Δ 0 EQ). In… Expand
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