Shoenfield is Gödel after Krivine

&
Mathematical Logic Quarterly 53 (2):176-179 (2007)
  Copy   BIBTEX

Abstract

We show that Shoenfield's functional interpretation of Peano arithmetic can be factorized as a negative translation due to J. L. Krivine followed by Gödel's Dialectica interpretation. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Categories

Keywords

Reprint years

DOI

10.1002/malq.200610038

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,322

External links

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

Through your library

My notes

Similar books and articles

Factorization of the Shoenfield-like Bounded Functional Interpretation.Jaime Gaspar - 2009 - Notre Dame Journal of Formal Logic 50 (1):53-60.
Storage operators and forall-positive types of system TTR.Karim Nour - 1996 - Mathematical Logic Quarterly 42:349-368.
Unifying Functional Interpretations.Paulo Oliva - 2006 - Notre Dame Journal of Formal Logic 47 (2):263-290.
Gödel's functional interpretation and its use in current mathematics.Ulrich Kohlenbach - 2008 - Dialectica 62 (2):223–267.
On the computational content of the Bolzano-Weierstraß Principle.Pavol Safarik & Ulrich Kohlenbach - 2010 - Mathematical Logic Quarterly 56 (5):508-532.
A General Type for Storage Operators.Karim Nour - 1995 - Mathematical Logic Quarterly 41 (4):505-514.
Functional interpretation and inductive definitions.Jeremy Avigad & Henry Towsner - 2009 - Journal of Symbolic Logic 74 (4):1100-1120.
An analysis of gödel's dialectica interpretation via linear logic.Paulo Oliva - 2008 - Dialectica 62 (2):269–290.
Gödel functional interpretation and weak compactness.Ulrich Kohlenbach - 2012 - Annals of Pure and Applied Logic 163 (11):1560-1579.
A note on the monotone functional interpretation.Ulrich Kohlenbach - 2011 - Mathematical Logic Quarterly 57 (6):611-614.
A Note on the Godel-Gentzen Translation.Hajime Ishihara - 2000 - Mathematical Logic Quarterly 46 (1):135-138.
Concepts and aims of functional interpretations: Towards a functional interpretation of constructive set theory.Wolfgang Burr - 2002 - Synthese 133 (1-2):257 - 274.
On the computational content of the axiom of choice.Stefano Berardi, Marc Bezem & Thierry Coquand - 1998 - Journal of Symbolic Logic 63 (2):600-622.
Temporal Gödel-Gentzen and Girard translations.Norihiro Kamide - 2013 - Mathematical Logic Quarterly 59 (1-2):66-83.
Gödel's Functional Interpretation.Jeremy Avigad & Solomon Feferman - 2000 - Bulletin of Symbolic Logic 6 (4):469-470.

Analytics

Added to PP
2013-12-01

Downloads
17 (#843,162)

6 months
7 (#425,192)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A functional interpretation for nonstandard arithmetic.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2012 - Annals of Pure and Applied Logic 163 (12):1962-1994.
Injecting uniformities into Peano arithmetic.Fernando Ferreira - 2009 - Annals of Pure and Applied Logic 157 (2-3):122-129.
Functional interpretation and inductive definitions.Jeremy Avigad & Henry Towsner - 2009 - Journal of Symbolic Logic 74 (4):1100-1120.

View all 16 citations / Add more citations

References found in this work

Opérateurs de mise en mémoire et traduction de Gödel.Jean-Louis Krivine - 1990 - Archive for Mathematical Logic 30 (4):241-267.
Proof theory in the abstract.J. M. E. Hyland - 2002 - Annals of Pure and Applied Logic 114 (1-3):43-78.

Add more references