Journal of Philosophical Logic

, Volume 26, Issue 3, pp 311–339 | Cite as

Elementary realizability

  • Zlatan Damnjanovic
Article

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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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Zlatan Damnjanovic
    • 1
  1. 1.School of PhylosophyUniversity of Southern CaliforniaLos AngelesU.S.A

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