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Elementary Realizability

Zlatan Damnjanovic
Journal of Philosophical Logic
Vol. 26, No. 3 (Jun., 1997), pp. 311-339
Published by: Springer
Stable URL: http://www.jstor.org/stable/30227096
Page Count: 29
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Elementary Realizability
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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.

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