Journal of Symbolic Logic 68 (3):1015-1043 (2003)

Joan Rand Moschovakis
Occidental College
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) is equivalent in A to ∃αA(α, β) for some stable A(α, β) (which belongs to the classical analytical hierarchy). The logic of A is intuitionistic. The axioms of A include countable comprehension, bar induction, Troelstra's generalized continuous choice, primitive recursive Markov's Principle and a classical axiom of dependent choices proposed by Krauss. Constructive dependent choices, and constructive and classical countable choice, are theorems, A is maximal with respect to classical Kleene function realizability, which establishes its consistency. The usual disjunction and (recursive) existence properties ensure that A preserves the constructive sense of "or" and "there exists."
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DOI 10.2178/jsl/1058448452
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References found in this work BETA

Foundations of Constructive Analysis.John Myhill - 1972 - Journal of Symbolic Logic 37 (4):744-747.
Analyzing Realizability by Troelstra's Methods.Joan Rand Moschovakis - 2002 - Annals of Pure and Applied Logic 114 (1-3):203-225.
Introduction to Metamathematics.H. Rasiowa - 1954 - Journal of Symbolic Logic 19 (3):215-216.
Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.

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Citations of this work BETA

Two Simple Sets That Are Not Positively Borel.Wim Veldman - 2005 - Annals of Pure and Applied Logic 135 (1-3):151-209.
The Double Negation of the Intermediate Value Theorem.Mohammad Ardeshir & Rasoul Ramezanian - 2010 - Annals of Pure and Applied Logic 161 (6):737-744.
Unavoidable Sequences in Constructive Analysis.Joan Rand Moschovakis - 2010 - Mathematical Logic Quarterly 56 (2):205-215.

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