2006/05/04 by Dmytro Taranovsky, Taranovsky, Dmytro
Computer Science · Mathematics · #03F55 #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03F55
paper · pdf · doi:10.48550/arxiv.math/0605138
23 pages; new results and references
openalex publication_date 2006/05/04 · arxiv created 2006/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.