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  1. Classical and constructive hierarchies in extended intuitionistic analysis.Joan Rand Moschovakis - 2003 - Journal of Symbolic Logic 68 (3):1015-1043.
    This paper introduces an extension A of Kleene's axiomatization of Brouwer's intuitionistic analysis, in which the classical arithmetical and analytical hierarchies are faithfully represented as hierarchies of the domains of continuity. A domain of continuity is a relation R(α) on Baire space with the property that every constructive partial functional defined on {α : R(α)} is continuous there. The domains of continuity for A coincide with the stable relations (those equivalent in A to their double negations), while every relation R(α) (...)
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