2005/02/23 by Bhupinder Singh Anand, Anand, Bhupinder Singh
Computer Science · Mathematics · #03B10 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematical and Theoretical Analysis #math.GM #msc:03B10
paper · pdf · doi:10.48550/arxiv.math/0502503
rev1; typos corrected in formulas; 5 pages; an HTML version is available at http://alixcomsi.com/An_arguable_inconsistency_in_ZF.htm
openalex publication_date 2005/02/23 · arxiv created 2005/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Classical theory proves that every primitive recursive function is strongly representable in PA; that formal Peano Arithmetic, PA, and formal primitive recursive arithmetic, PRA, can both be interpreted in Zermelo-Fraenkel Set Theory, ZF; and that if ZF is consistent, then PA+PRA is consistent. We show that PA+PRA is inconsistent; it follows that ZF, too, is inconsistent.