Journal of Philosophical Logic 26 (3):311-339 (1997)
Authors |
|
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
|
Keywords | Philosophy |
Categories | (categorize this paper) |
Reprint years | 2004 |
DOI | 10.1023/A:1017994504149 |
Options |
![]() ![]() ![]() ![]() |
Download options
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.
Strictly Primitive Recursive Realizability, II. Completeness with Respect to Iterated Reflection and a Primitive Recursive $\omega$ -Rule.Zlatan Damnjanovic - 1998 - Notre Dame Journal of Formal Logic 39 (3):363-388.
Elementary Functions and LOOP Programs.Zlatan Damnjanovic - 1994 - Notre Dame Journal of Formal Logic 35 (4):496-522.
Similar books and articles
Relating First-Order Set Theories and Elementary Toposes.Steve Awodey, Carsten Butz & Alex Simpson - 2007 - Bulletin of Symbolic Logic 13 (3):340-358.
Strictly Primitive Recursive Realizability, I.Zlatan Damnjanovic - 1994 - Journal of Symbolic Logic 59 (4):1210-1227.
On the Elementary Theory of Restricted Elementary Functions.Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (3):796-808.
On the Elementary Theory of Restricted Elementary Functions.Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (3):796 - 808.
A Model of Peano Arithmetic with No Elementary End Extension.George Mills - 1978 - Journal of Symbolic Logic 43 (3):563-567.
On Kleene's Recursive Realizability as an Interpretation for Intuitionistic Elementary Number Theory.Robert R. Tompkins - 1968 - Notre Dame Journal of Formal Logic 9 (4):289-293.
Elementary Functions and LOOP Programs.Zlatan Damnjanovic - 1994 - Notre Dame Journal of Formal Logic 35 (4):496-522.
Minimal Realizability of Intuitionistic Arithmetic and Elementary Analysis.Zlatan Damnjanovic - 1995 - Journal of Symbolic Logic 60 (4):1208-1241.
Analytics
Added to PP index
2009-01-28
Total views
79 ( #146,513 of 2,506,009 )
Recent downloads (6 months)
1 ( #416,828 of 2,506,009 )
2009-01-28
Total views
79 ( #146,513 of 2,506,009 )
Recent downloads (6 months)
1 ( #416,828 of 2,506,009 )
How can I increase my downloads?
Downloads