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

Article information

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

basic arithmetic primitive recursive realizability polynomially bounded realizability


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.

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