Notre Dame Journal of Formal Logic

A Counterexample to Polynomially Bounded Realizability of Basic Arithmetic

Mohammad Ardeshir, Erfan Khaniki, and Mohsen Shahriari

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Abstract

We give a counterexample to the claim that every provably total function of Basic Arithmetic is a polynomially bounded primitive recursive function.

Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 481-489.

Dates
Received: 16 March 2016
Accepted: 6 November 2017
First available in Project Euclid: 4 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1562205626

Digital Object Identifier
doi:10.1215/00294527-2019-0013

Mathematical Reviews number (MathSciNet)
MR3985622

Subjects
Primary: 03F30: First-order arithmetic and fragments
Secondary: 03F50: Metamathematics of constructive systems

Keywords
basic arithmetic primitive recursive realizability polynomially bounded realizability

Citation

Ardeshir, Mohammad; Khaniki, Erfan; Shahriari, Mohsen. A Counterexample to Polynomially Bounded Realizability of Basic Arithmetic. Notre Dame J. Formal Logic 60 (2019), no. 3, 481--489. doi:10.1215/00294527-2019-0013. https://projecteuclid.org/euclid.ndjfl/1562205626


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References

  • [1] Ardeshir, M. and B. Hesaam, “An introduction to basic arithmetic,” Logic Journal of the IGPL, vol. 16 (2008), pp. 1–13.
  • [2] Ruitenburg, W., “Basic predicate calculus,” Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 18–46.
  • [3] Salehi, S., “Provably total functions of Basic Arithmetic,” Mathematical Logic Quarterly (MLQ), vol. 49 (2003), pp. 316–22.
  • [4] Salehi, S., “Polynomially bounded recursive realizability,” Notre Dame Journal of Formal Logic, vol. 46 (2005), pp. 407–17.
  • [5] Zagier, D., “Newman’s short proof of the prime number theorem,” American Mathematical Monthly, vol. 104 (1997), pp. 705–08.