Journal of Philosophical Logic

, Volume 26, Issue 3, pp 311–339

Elementary realizability

Authors

  • Zlatan Damnjanovic
    • School of PhylosophyUniversity of Southern California
Article

DOI: 10.1023/A:1017994504149

Cite this article as:
Damnjanovic, Z. Journal of Philosophical Logic (1997) 26: 311. doi:10.1023/A:1017994504149
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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.

Copyright information

© Kluwer Academic Publishers 1997