Indecomposability of negative dense subsets of ℝ in Constructive Reverse Mathematics

Logic Journal of the IGPL 17 (2):173-177 (2009)
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Abstract

In 1970 Vesley proposed a substitute of Kripke's Scheme. In this paper it is shown that —over Bishop's constructive mathematics— the indecomposability of negative dense subsets of ℝ is equivalent to a weakening of Vesley's proposal. This result supports the idea that full Kripke's Scheme might not be necessary for most of intuitionistic mathematics. At the same time it contributes to the programme of Constructive Reverse Mathematics and gives a new answer to a 1997 question of Van Dalen

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Iris Loeb
VU University Amsterdam

Citations of this work

Connectedness of the Continuum in Intuitionistic Mathematics.Mark Bickford - 2018 - Mathematical Logic Quarterly 64 (4-5):387-394.

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References found in this work

Relative Constructivity.Ulrich Kohlenbach - 1998 - Journal of Symbolic Logic 63 (4):1218-1238.
Continuity Properties in Constructive Mathematics.Hajime Ishihara - 1992 - Journal of Symbolic Logic 57 (2):557-565.
How Connected is the Intuitionistic Continuum?Dirk Van Dalen - 1997 - Journal of Symbolic Logic 62 (4):1147 - 1150.
A Palatable Substitute for Kripke's Schema.R. E. Vesley, A. Kino & J. Myhill - 1974 - Journal of Symbolic Logic 39 (2):334-334.

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