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A continuity principle, a version of Baire's theorem and a boundedness principle

  • Hajime Ishihara (a1) and Peter Schuster (a2)
Abstract
Abstract

We deal with a restricted form WC-N′ of the weak continuity principle, a version BT′ of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N′, BT′ + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

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[2] Errett Bishop and Douglas Bridges , Constructive analysis, Springer, Berlin, 1985.

[3] Douglas Bridges , Hajime Ishihara , Peter Schuster , and Luminiţa Vîţă , Strong continuity implies uniformly sequential continuity. Archive for Mathematical Logic, vol. 44 (2005), pp. 887895.

[4] Douglas Bridges , Hajime Ishihara , and Luminiţa Vîţă , A new constructive version of Baire's theorem, Hokkaido Mathematical Journal, vol. 35 (2006), pp. 107118.

[5] Douglas Bridges and Fred Richman , Varieties of constructive mathematics, London Mathematical Society Lecture Notes Series, vol. 97, Cambridge University Press, London, 1987.

[6] Douglas Bridges and Luminiţa Vîţă , Techniques of constructive analysis, Springer, New York, 2006.

[9] Hajime Ishihara , Sequential continuity in constructive mathematics. Combinatorics, computability and logic ( C. S. Calude . M. J. Dinneen , and S. Sburlan , editors). Springer-Verlag, London, 2001, pp. 512.

[10] Hajime Ishihara , Constructive reverse mathematics: compactness properties, From sets and types to analysis and topology ( L. Crosilla and P. Schuster , editors), Oxford Logic Guides 48, Oxford University Press, 2005, pp. 245267.

[14] Iris Loeb , Equivalents of the (weak) fan theorem, Annals of Pure and Applied Logic, vol, 132 (2005), pp. 5166.

[15] Sara Negri and Daniele Soravia , The continuum as a formal space, Archive for Mathematical Logic, vol. 38 (1999), pp. 423447.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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