Journal of Philosophical Logic 26 (3):311-339 (1997)
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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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| Keywords | Philosophy |
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| Reprint years | 2004 |
| DOI | 10.1023/A:1017994504149 |
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References found in this work BETA
Functional Interpretations of Feasibly Constructive Arithmetic.Stephen Cook & Alasdair Urquhart - 1993 - Annals of Pure and Applied Logic 63 (2):103-200.
View all 11 references / Add more references
Citations of this work BETA
Polynomially Bounded Recursive Realizability.Saeed Salehi - 2005 - Notre Dame Journal of Formal Logic 46 (4):407-417.
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Elementary Functions and LOOP Programs.Zlatan Damnjanovic - 1994 - Notre Dame Journal of Formal Logic 35 (4):496-522.
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