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Constructive Mathematical Truth

Dmytro Taranovsky
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Abstract

We define constructive truth for arithmetic and for intuitionistic analysis, and investigate its properties. We also prove that the set of constructively true (first order) arithmetical statements is Pi-1-2 and Sigma-1-2 hard, and we conjecture it to be complete for second order arithmetic. A statement is constructively true iff it is realized by a constructive function under continuous function realizability.

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Dmytro Taranovsky. 2006-06-01. Constructive Mathematical Truth. https://arxiv.org/abs/math/0605138

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