Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/provably-recursive-functions-of-constructive-and-relatively-Il0lW4yOuv
References (19)
-
J. Avigad (2004)
Forcing in Proof TheoryBulletin of Symbolic Logic, 10
-
J. Avigad (2000)
Interpreting classical theories in constructive onesJournal of Symbolic Logic, 65
-
S. Buss (1993)
A note on bootstrapping intuitionistic bounded arithmetic -
S.R. Buss (1992)
A Note on Bootstrapping Intuitionistic Bounded Arithmetic, Proof Theory (Leeds, 1990) -
D. Leivant (1985)
Syntactic translations and provably total functionsJ. Symb. Log., 50
-
T. Coquand, M. Hofmann (1999)
A new method for establishing conservativity of classical systems over their intuitionistic versionMathematical Structures in Computer Science, 9
-
K.F. Wehmeier (1997)
Fragments of HA based on Σ1-inductionArch. Math. Log., 37
-
V. Harnik (1992)
Provably total functions of intuitionistic bounded arithmeticJournal of Symbolic Logic, 57
-
S. Cook, A. Urquhart (1989)
Functional interpretations of feasibly constructive arithmeticAnn. Pure Appl. Log., 63
-
W. Burr (2000)
Fragments of Heyting arithmeticJournal of Symbolic Logic, 65
-
A. Troelstra, D. Dalen, A. Heyting (1988)
Constructivism in Mathematics: An Introduction -
A. Troelstra, H. Schwichtenberg (1996)
Basic proof theory, 43
-
R. Parikh (1971)
Existence and feasibility in arithmeticJournal of Symbolic Logic, 36
-
Morteza Moniri (2003)
On two questions about feasibly constructive arithmeticMathematical Logic Quarterly, 49
-
S. Berardi (2004)
A generalization of a conservativity theorem for classical versus intuitionistic arithmeticMathematical Logic Quarterly, 50
-
Morteza Moniri (2003)
Comparing Constructive Arithmetical Theories Based on NP-PIND and coNP-PINDJ. Log. Comput., 13
-
D. Leivant (1985)
Syntactic translations and provably recursive functionsJournal of Symbolic Logic, 50
-
Morteza Moniri (2008)
On the Hierarchy of Intuitionistic Bounded ArithmeticJ. Log. Comput., 18
-
K. Wehmeier (1997)
Fragments of $HA$ based on $\Sigma_1$-inductionArchive for Mathematical Logic, 37
- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer-Verlag
- Subject
- Mathematics; Algebra; Mathematics, general; Mathematical Logic and Foundations
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-009-0172-0
- Publisher site
- See Article on Publisher Site
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.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Dec 24, 2009