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An induction principle over real numbers

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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.

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References

  1. Coquand, T.: A note on the open induction principle. http://www.math.chalmers.se/~coquand/intuitionnism.html (1997)

  2. 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)

  3. Raoult, J.C.: Induction of open properties. Research Report RR-0813, INRIA (1988). https://hal.inria.fr/inria-00075738

  4. Troelstra, A. (ed.): Metamathematical Investigation of Intutitionnistic Arithmetic and Analysis, Lecture Notes in Mathematics, vol. 344. Springer, Berlin (1973)

  5. 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)

  6. 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)

  7. Veldman, W.: Almost the fan theorem. Nieuw Arch. Wiskd. (5) 2(4) (2001)

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Correspondence to Assia Mahboubi.

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Mahboubi, A. An induction principle over real numbers. Arch. Math. Logic 56, 43–49 (2017). https://doi.org/10.1007/s00153-016-0513-8

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  • DOI: https://doi.org/10.1007/s00153-016-0513-8

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