Predicative functionals and an interpretation of ID<ω

In 1958 Gödel published his Dialectica interpretation, which reduces classical arithmetic to a quantifier-free theory T axiomatizing the primitive recursive functionals of finite type. Here we extend Gödel's T to theories Pn of “predicative” functionals, which are defined using Martin-Löf's universes of transfinite types. We then extend Gödel's interpretation to the theories of arithmetic inductive definitions IDn, so that each IDn is interpreted in the corresponding Pn. Since the strengths of the theories IDn are cofinal in the ordinal Γ0, as a corollary this analysis provides an ordinal-free characterization of the <Γ0-recursive functions
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1016/S0168-0072(97)00045-6
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,667
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Justus Diller (2002). Logical Problems of Functional Interpretations. Annals of Pure and Applied Logic 114 (1-3):27-42.

Add more citations

Similar books and articles
Ulrich Kohlenbach (1999). On the No-Counterexample Interpretation. Journal of Symbolic Logic 64 (4):1491-1511.
Fernando Ferreira (2008). A Most Artistic Package of a Jumble of Ideas. Dialectica 62 (2: Table of Contents"/> Select):205–222.
William Tait (2006). Godel's Interpretation of Intuitionism. Philosophia Mathematica 14 (2):208-228.

Monthly downloads

Added to index


Total downloads

7 ( #304,000 of 1,726,249 )

Recent downloads (6 months)

4 ( #183,615 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.