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On the Disjunctive Markov Principle

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Abstract

In this note we show that over a strong (semi-)intuitionistic base theory, the recursive comprehension principle \({\Delta^0_1}\) -CA does not imply the disjunctive Markov principle MP\({^{\vee}}\).

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References

  1. Akama, Y., S. Berardi, S. Hayashi, and U. Kohlenbach, An arithmetical hierarchy of the law of excluded middle and related principles, in Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS’04), pp. 192–201, IEEE Press 2004.

  2. Fujiwara, M., H. Ishihara, and T. Nemoto,Some principles weaker than Markov’s principle. To appear in: Arch. Math. Logic.

  3. Ishihara, H., Markov’s principle, Church’s thesis and Lindelöf’s theorem. Indagationes Mathematicae, N.S. 4:321–325, 1993.

  4. Kohlenbach, U., Applied proof theory: Proof interpretations and their use in math ematics. Springer Monographs in Mathematics. xx+536pp., Springer Heidelberg, 2008.

  5. Troelstra, A.S. (ed.) Metamathematical investigation of intuitionistic arithmetic and analysis. Springer Lecture Notes in Mathematics 344, 1973.

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Correspondence to Ulrich Kohlenbach.

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Presented by Daniele Mundici

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Kohlenbach, U. On the Disjunctive Markov Principle. Stud Logica 103, 1313–1317 (2015). https://doi.org/10.1007/s11225-015-9627-y

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  • DOI: https://doi.org/10.1007/s11225-015-9627-y

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