Countable choice as a questionable uniformity principle

Philosophia Mathematica 12 (2):106-134 (2004)

Abstract

Should weak forms of the axiom of choice really be accepted within constructive mathematics? A critical view of the Brouwer-Heyting-Kolmogorov interpretation, accompanied by the intention to include nondeterministic algorithms, leads us to subscribe to Richman's appeal for dropping countable choice. As an alternative interpretation of intuitionistic logic, we propose to renew dialogue semantics.

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Peter Schuster
University of Leeds

References found in this work

Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Tractatus Logico-Philosophicus.Ludwig Wittgenstein - 1956 - Revista Portuguesa de Filosofia 12 (1):109-110.
The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - Cambridge University Press.
Foundations of Constructive Analysis.John Myhill - 1972 - Journal of Symbolic Logic 37 (4):744-747.

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Citations of this work

Choice Principles and Constructive Logics.David Dedivi - 2004 - Philosophia Mathematica 12 (3):222-243.

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