Abstract
We give a constructive proof of the open induction principle on real numbers, using bar induction and enumerative open sets. We comment the algorithmic content of this result.
Similar content being viewed by others
References
Coquand, T.: A note on the open induction principle. http://www.math.chalmers.se/~coquand/intuitionnism.html (1997)
Geuvers, H., Niqui, M.: Constructive reals in coq: axioms and categoricity. In: Types for Proofs and Programs, International Workshop, TYPES 2000, Durham, UK, December 8–12, 2000, Selected Papers, Lecture Notes in Computer Science, vol. 2277, pp. 79–95. Springer, Berlin (2000)
Raoult, J.C.: Induction of open properties. Research Report RR-0813, INRIA (1988). https://hal.inria.fr/inria-00075738
Troelstra, A. (ed.): Metamathematical Investigation of Intutitionnistic Arithmetic and Analysis, Lecture Notes in Mathematics, vol. 344. Springer, Berlin (1973)
Troelstra, A.S., van Dalen, D.: Constructivism in mathematics. Vol. I, Studies in Logic and the Foundations of Mathematics, An Introduction, vol. 121. North-Holland Publishing Co., Amsterdam (1988)
Troelstra, A.S., van Dalen, D.: Constructivism in mathematics. Vol. II, Studies in Logic and the Foundations of Mathematics, An Introduction, vol. 123. North-Holland Publishing Co., Amsterdam (1988)
Veldman, W.: Almost the fan theorem. Nieuw Arch. Wiskd. (5) 2(4) (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mahboubi, A. An induction principle over real numbers. Arch. Math. Logic 56, 43–49 (2017). https://doi.org/10.1007/s00153-016-0513-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-016-0513-8