Abstract
We show that the computational interpretation of full comprehension via two well-known functional interpretations (dialectica and modified realizability) corresponds to two closely related infinite products of selection functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Avigad, J., Feferman, S.: Gödel’s functional (“Dialectica”) interpretation. In: Buss, S.R. (ed.) Handbook of proof theory. Studies in Logic and the Foundations of Mathematics, vol. 137, pp. 337–405. North Holland, Amsterdam (1998)
Berardi, S., Bezem, M., Coquand, T.: On the computational content of the axiom of choice. The Journal of Symbolic Logic 63(2), 600–622 (1998)
Berger, U., Oliva, P.: Modified bar recursion and classical dependent choice. Lecture Notes in Logic 20, 89–107 (2005)
Berger, U., Oliva, P.: Modified bar recursion. Mathematical Structures in Computer Science 16, 163–183 (2006)
Berger, U., Schwichtenberg, H.: Program extraction from classical proofs. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 77–97. Springer, Heidelberg (1995)
Bezem, M.: Strongly majorizable functionals of finite type: a model for bar recursion containing discontinuous functionals. The Journal of Symbolic Logic 50, 652–660 (1985)
Escardó, M.H.: Infinite sets that admit fast exhaustive search. In: Proceedings of LICS, pp. 443–452 (2007)
Escardó, M.H., Oliva, P.: The Peirce translation and the double negation shift. In: Ferreira, F., Lowe, B., Mayordomo, E., Gomes, L.M. (eds.) CiE 2010. LNCS, vol. 6158, pp. 151–161. Springer, Heidelberg (2010)
Escardó, M.H., Oliva, P.: Selection functions, bar recursion, and backward induction. Mathematical Structures in Computer Science 20(2), 127–168 (2010)
Gödel, K.: Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica 12, 280–287 (1958)
Kohlenbach, U.: Higher order reverse mathematics. In: Simpson, S.G. (ed.) Reverse Mathematics 2001, ASL, A.K. Peters. Lecture Notes in Logic, vol. 21, pp. 281–295 (2005)
Kohlenbach, U.: Applied Proof Theory: Proof Interpretations and their Use in Mathematics. In: Monographs in Mathematics. Springer, Heidelberg (2008)
Normann, D.: The continuous functionals. In: Griffor, E.R. (ed.) Handbook of Computability Theory, ch. 8, pp. 251–275. North Holland, Amsterdam (1999)
Spector, C.: Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles in current intuitionistic mathematics. In: Dekker, F.D.E. (ed.) Recursive Function Theory: Proc. Symposia in Pure Mathematics, vol. 5, pp. 1–27. American Mathematical Society, Providence (1962)
Troelstra, A.S.: Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. LNM, vol. 344. Springer, Berlin (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Escardó, M., Oliva, P. (2010). Computational Interpretations of Analysis via Products of Selection Functions. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-13962-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13961-1
Online ISBN: 978-3-642-13962-8
eBook Packages: Computer ScienceComputer Science (R0)