Dialectica interpretation of well-founded induction

Mathematical Logic Quarterly

Volumn 54, Issue 3, 2008, Pages 229-239

  Schwichtenberg, Helmut ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Dialectica interpretation; Euclid's theorem; Program extraction

Indexed keywords

EID: 55549089706     PISSN: 09425616     EISSN: 15213870     Source Type: Journal    
DOI: 10.1002/malq.200710045     Document Type: Conference Paper

References (10)

1. U. Berger, W. Buchholz, and H. Schwichtenberg, Refined program extraction from classical proofs. Annals Pure Applied Logic 114, 3-25 (2002).
2. U. Berger, M. Eberl, and H. Schwichtenberg, Term rewriting for normalization by evaluation. Information and Computation 183, 19-42 (2003).
3. U. Berger and H. Schwichtenberg, The greatest common divisor: a case study for program extraction from classical proofs. In: Types for Proofs and Programs. International Workshop TYPES '95, Torino, Italy, June 1995. Selected Papers (S. Berardi and M. Coppo, eds.). Lecture Notes in Computer Science 1158, pp. 36-46 (Springer-Verlag, 1996).
4. A. Dragalin, New kinds of realizability. In: Abstracts of the 6th International Congress of Logic, Methodology and Philosophy of Sciences, pp. 20-24, Hannover, Germany, 1979.
5. H. Friedman, Classically and intuitionistically provably recursive functions. In: Higher Set Theory (D. Scott and G. Müller, eds.). Lecture Notes in Mathematics 669, pp. 21-28 (Springer-Verlag, 1978).
6. K. Gödel, Über eine bisher noch nicht benützte Erweiterung des finiten Standpunkts. Dialectica 12, 280-287 (1958).
7. M.-D. Hernest, Feasible programs from (non-constructive) proofs by the light (monotone) Dialectica interpretation. Ph. D. thesis, Ecole Polytechnique Paris and LMU München, 2006.
8. K. F. Jørgensen, Finite type arithmetic. Master's thesis, University of Roskilde, 2001.
9. H. Schwichtenberg and S. S. Wainer, Ordinal bounds for programs. In: Feasible Mathematics II (P. Clote and J. Remmel, eds.), pp. 387-406 (Birkhäuser, 1995).
10. A. S. Troelstra (ed.), Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Lecture Notes in Mathematics 344 (Springer-Verlag, 1973).