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  1. The development of intuitionistic logic.Mark van Atten - 2008 - Stanford Encyclopedia of Philosophy.
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  • The fine structure of the intuitionistic borel hierarchy.Wim Veldman - 2009 - Review of Symbolic Logic 2 (1):30-101.
    In intuitionistic analysis, a subset of a Polish space like or is called positively Borel if and only if it is an open subset of the space or a closed subset of the space or the result of forming either the countable union or the countable intersection of an infinite sequence of (earlier constructed) positively Borel subsets of the space. The operation of taking the complement is absent from this inductive definition, and, in fact, the complement of a positively Borel (...)
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  • Brouwer’s Fan Theorem as an axiom and as a contrast to Kleene’s alternative.Wim Veldman - 2014 - Archive for Mathematical Logic 53 (5):621-693.
    The paper is a contribution to intuitionistic reverse mathematics. We introduce a formal system called Basic Intuitionistic Mathematics BIM, and then search for statements that are, over BIM, equivalent to Brouwer’s Fan Theorem or to its positive denial, Kleene’s Alternative to the Fan Theorem. The Fan Theorem is true under the intended intuitionistic interpretation and Kleene’s Alternative is true in the model of BIM consisting of the Turing-computable functions. The task of finding equivalents of Kleene’s Alternative is, intuitionistically, a nontrivial (...)
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