Provably recursive functions of constructive and relatively constructive theories

Archive for Mathematical Logic 49 (3):291-300 (2010)

Abstract

In this paper we prove conservation theorems for theories of classical first-order arithmetic over their intuitionistic version. We also prove generalized conservation results for intuitionistic theories when certain weak forms of the principle of excluded middle are added to them. Members of two families of subsystems of Heyting arithmetic and Buss-Harnik’s theories of intuitionistic bounded arithmetic are the intuitionistic theories we consider. For the first group, we use a method described by Leivant based on the negative translation combined with a variant of Friedman’s translation. For the second group, we use Avigad’s forcing method

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,743

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2013-11-23

Downloads
18 (#614,101)

6 months
1 (#387,390)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

References found in this work

Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
Existence and Feasibility in Arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Interpreting Classical Theories in Constructive Ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.

View all 12 references / Add more references

Citations of this work

No citations found.

Add more citations

Similar books and articles

Interpreting Classical Theories in Constructive Ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.
Polynomially Bounded Recursive Realizability.Saeed Salehi - 2005 - Notre Dame Journal of Formal Logic 46 (4):407-417.
Preservation Theorems for Bounded Formulas.Morteza Moniri - 2007 - Archive for Mathematical Logic 46 (1):9-14.
A Realizability Interpretation for Classical Arithmetic.Jeremy Avigad - 2002 - Bulletin of Symbolic Logic 8 (3):439-440.
Closed Fragments of Provability Logics of Constructive Theories.Albert Visser - 2008 - Journal of Symbolic Logic 73 (3):1081-1096.
Models of Intuitionistic TT and N.Daniel Dzierzgowski - 1995 - Journal of Symbolic Logic 60 (2):640-653.
Forcing in Proof Theory.Jeremy Avigad - 2004 - Bulletin of Symbolic Logic 10 (3):305-333.
On Two Questions About Feasibly Constructive Arithmetic.Morteza Moniri - 2003 - Mathematical Logic Quarterly 49 (4):425.