Indecomposability of ℝ and ℝ \ {0} in Constructive Reverse Mathematics

Logic Journal of the IGPL 16 (3):269-273 (2008)
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Abstract

It is shown that—over Bishop's constructive mathematics—the indecomposability of ℝ is equivalent to the statement that all functions from a complete metric space into a metric space are sequentially nondiscontinuous. Furthermore we prove that the indecomposability of ℝ \ {0} is equivalent to the negation of the disjunctive version of Markov's Principle. These results contribute to the programme of Constructive Reverse Mathematics

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10.1093/jigpal/jzn006

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Iris Loeb
VU University Amsterdam

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Connectedness of the continuum in intuitionistic mathematics.Mark Bickford - 2018 - Mathematical Logic Quarterly 64 (4-5):387-394.

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