, Volume 26, Issue 3, pp 311-339

Elementary realizability

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

A realizability notion that employs only Kalmar elementary functions is defined, and, relative to it, the soundness of EA-(Π10-IR), a fragment of Heyting Arithmetic (HA) with names and axioms for all elementary functions and induction rule restricted to Π10 formulae, is proved. As a corollary, it is proved that the provably recursive functions of EA-(Π10-IR) are precisely the elementary functions. Elementary realizability is proposed as a model of strict arithmetic constructivism, which allows only those constructive procedures for which the amount of computational resources required can be bounded in advance.