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Logic Journal of IGPL Advance Access published online on March 6, 2008
Logic Journal of IGPL, doi:10.1093/jigpal/jzn006
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

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

Iris Loeb

Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand. E-mail: I.Loeb{at}math.canterbury.ac.nz


  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.

Key Words: Indecomposability • Constructive Reverse Mathematics • Continuity Principles • Disjunctive Version of Markov's Principle

Received for publication 7 September 2007.
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