Constructive Mathematical Truth
Logic
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0605138,
title = {Constructive Mathematical Truth},
author = {Dmytro Taranovsky},
journal= {arXiv preprint arXiv:math/0605138},
year = {2007}
}
Comments
23 pages; new results and references